LCM and HCF - Wikitechy https://www.wikitechy.com/interview-questions/category/lcm-and-hcf/ Interview Questions Mon, 20 Sep 2021 10:24:00 +0000 en-US hourly 1 https://wordpress.org/?v=6.9 https://www.wikitechy.com/interview-questions/wp-content/uploads/2025/10/cropped-wikitechy-icon-32x32.png LCM and HCF - Wikitechy https://www.wikitechy.com/interview-questions/category/lcm-and-hcf/ 32 32 What is the LCM of 147/64 and 30/44 ? https://www.wikitechy.com/interview-questions/lcm-and-hcf/what-is-the-lcm-of-147-64-and-30-44/ https://www.wikitechy.com/interview-questions/lcm-and-hcf/what-is-the-lcm-of-147-64-and-30-44/#respond Tue, 17 Aug 2021 17:57:35 +0000 https://www.wikitechy.com/interview-questions/?p=1847

What is the LCM of 147/64 and 30/44 ?

A. 735/704

B. 3/704

C. 735/2

D. 3/735

Answer : C. 735/2

Explanation:

Find the LCM of the Numerators.
LCM (147, 30) = 1470
Find the HCF of Denominators.
HCF (64, 44) = 4
So, the LCM of 147/64 and 30/44 is (LCM of Numerators) / (HCF of Denominators) = 1470 / 4 = 735/2

]]> https://www.wikitechy.com/interview-questions/lcm-and-hcf/what-is-the-lcm-of-147-64-and-30-44/feed/ 0 What is the smallest number that leaves a remainder of 2 when divided by 3, 4, 5, and 6 ? https://www.wikitechy.com/interview-questions/lcm-and-hcf/what-is-the-smallest-number-that-leaves-a-remainder-of-2-when-divided-by-3-4-5-and-6/ https://www.wikitechy.com/interview-questions/lcm-and-hcf/what-is-the-smallest-number-that-leaves-a-remainder-of-2-when-divided-by-3-4-5-and-6/#respond Tue, 17 Aug 2021 17:56:25 +0000 https://www.wikitechy.com/interview-questions/?p=1846 What is the smallest number that leaves a remainder of 2 when divided by 3, 4, 5, and 6 ?

A. 56

B. 128

C. 62

D. 32

Answer : C. 62

Explanation:

Take the lcm of 3 , 4 , 5 , 6.
3 = 3×1
4 = 2×2
5 = 5×1
6 = 2×3
LCM = 2 × 2 × 3 × 5 = 60
Therefore 60 is the number that is completely divisible by these numbers. But we have to find the smallest number that leaves remainder 2.
Answer : 60 + 2 = 62

]]> https://www.wikitechy.com/interview-questions/lcm-and-hcf/what-is-the-smallest-number-that-leaves-a-remainder-of-2-when-divided-by-3-4-5-and-6/feed/ 0 Find the smallest 4 digit number which is divisible by 18, 24, 32 ? https://www.wikitechy.com/interview-questions/lcm-and-hcf/find-the-smallest-4-digit-number-which-is-divisible-by-18-24-32/ https://www.wikitechy.com/interview-questions/lcm-and-hcf/find-the-smallest-4-digit-number-which-is-divisible-by-18-24-32/#respond Tue, 17 Aug 2021 17:54:58 +0000 https://www.wikitechy.com/interview-questions/?p=1845

Find the smallest 4 digit number which is divisible by 18, 24, 32 ?

A. 1216

B. 1512

C. 1152

D. 1680

Answer : C. 1152

Explanation:

LCM of 18, 24 and 32:
–> 18 = 2 x 3 x 3
–> 24 = 2 x 2 x 2 x 3
–> 32 = 2 x 2 x 2 x 2 x 2
LCM = 2 x 2 x 2 x 2 x 2 x 3 x 3 = 288.

The smallest four digit number that is divisible by 288:
288 x 3 = 864
288 x 4 = 1152

Since 288 is divisible by 18, 24 and 32, 1152 is also divisible by all these numbers. Therefore, 1152 is the smallest four digit number divisible by 18, 24 and 32.

]]> https://www.wikitechy.com/interview-questions/lcm-and-hcf/find-the-smallest-4-digit-number-which-is-divisible-by-18-24-32/feed/ 0 There are three numbers, these are co-prime to each other are such that the product of the first two is 551 and that of the last two is 1073. What will be the sum of three numbers ? https://www.wikitechy.com/interview-questions/lcm-and-hcf/there-are-three-numbers-these-are-co-prime-to-each-other-are-such-that-the-product-of-the-first-two-is-551-and-that-of-the-last-two-is-1073-what-will-be-the-sum-of-three-numbers/ https://www.wikitechy.com/interview-questions/lcm-and-hcf/there-are-three-numbers-these-are-co-prime-to-each-other-are-such-that-the-product-of-the-first-two-is-551-and-that-of-the-last-two-is-1073-what-will-be-the-sum-of-three-numbers/#respond Tue, 17 Aug 2021 17:53:18 +0000 https://www.wikitechy.com/interview-questions/?p=1844

There are three numbers, these are co-prime to each other are such that the product of the first two is 551 and that of the last two is 1073. What will be the sum of three numbers ?

A. 67

B. 85

C. 129

D. 87

Answer : B. 85

Explanation:

Since the numbers are co-prime, they contain only 1 as the common factor.
It is also given that two products have the middle number in common.
So, middle number = H.C.F. of 551 and 1073 = 29.
So, First number is = 551/29 = 19.
Third number = 1073/29 = 37
So sum of these numbers is = (19 + 29 + 37) = 85.

]]> https://www.wikitechy.com/interview-questions/lcm-and-hcf/there-are-three-numbers-these-are-co-prime-to-each-other-are-such-that-the-product-of-the-first-two-is-551-and-that-of-the-last-two-is-1073-what-will-be-the-sum-of-three-numbers/feed/ 0 Six bells commence tolling together and toll at the intervals of 2, 4, 6, 8, 10, 12 seconds respectively. In 60 minutes how many times they will toll together ? https://www.wikitechy.com/interview-questions/lcm-and-hcf/six-bells-commence-tolling-together-and-toll-at-the-intervals-of-2-4-6-8-10-12-seconds-respectively-in-60-minutes-how-many-times-they-will-toll-together/ https://www.wikitechy.com/interview-questions/lcm-and-hcf/six-bells-commence-tolling-together-and-toll-at-the-intervals-of-2-4-6-8-10-12-seconds-respectively-in-60-minutes-how-many-times-they-will-toll-together/#respond Tue, 17 Aug 2021 17:50:52 +0000 https://www.wikitechy.com/interview-questions/?p=1843

Six bells commence tolling together and toll at the intervals of 2, 4, 6, 8, 10, 12 seconds respectively. In 60 minutes how many times they will toll together ?

A. 16

B. 15

C. 31

D. 30

Answer : C. 31

Explanation:

LCM of 2 , 4 , 6 ,8 , 10 , 12 is 120 seconds, that’s 2 minutes.
Now 60 / 2 = 30
Adding one bell at the beginning it’ll be 30 + 1 = 31.

]]> https://www.wikitechy.com/interview-questions/lcm-and-hcf/six-bells-commence-tolling-together-and-toll-at-the-intervals-of-2-4-6-8-10-12-seconds-respectively-in-60-minutes-how-many-times-they-will-toll-together/feed/ 0 Find the greatest number which on dividing 1661 and 2045, leaves a remainder of 10 and 13 respectively ? https://www.wikitechy.com/interview-questions/lcm-and-hcf/find-the-greatest-number-which-on-dividing-1661-and-2045-leaves-a-remainder-of-10-and-13-respectively/ https://www.wikitechy.com/interview-questions/lcm-and-hcf/find-the-greatest-number-which-on-dividing-1661-and-2045-leaves-a-remainder-of-10-and-13-respectively/#respond Tue, 17 Aug 2021 17:48:26 +0000 https://www.wikitechy.com/interview-questions/?p=1842

Find the greatest number which on dividing 1661 and 2045, leaves a remainder of 10 and 13 respectively ?

A. 91

B. 127

C. 137

D. 140

Answer : B . 127

Explanation:

In this type of question, we need to calculate the HCF, trick is,
HCF (1661 – 10) and (2045 -13)
= HCF (1651, 2032)
= 127

]]> https://www.wikitechy.com/interview-questions/lcm-and-hcf/find-the-greatest-number-which-on-dividing-1661-and-2045-leaves-a-remainder-of-10-and-13-respectively/feed/ 0 Which greatest possible length can be used to measure exactly 15 meter 75 cm, 11 meter 25 cm and 7 meter 65 cm ? https://www.wikitechy.com/interview-questions/lcm-and-hcf/which-greatest-possible-length-can-be-used-to-measure-exactly-15-meter-75-cm-11-meter-25-cm-and-7-meter-65-cm/ https://www.wikitechy.com/interview-questions/lcm-and-hcf/which-greatest-possible-length-can-be-used-to-measure-exactly-15-meter-75-cm-11-meter-25-cm-and-7-meter-65-cm/#respond Tue, 17 Aug 2021 17:46:33 +0000 https://www.wikitechy.com/interview-questions/?p=1841

Which greatest possible length can be used to measure exactly 15 meter 75 cm, 11 meter 25 cm & 7 meter 65 cm ?

A. 45

B. 255

C. 55

D. 36

Answer : A. 45

Explanation:

The HCF for given length.
–> 15 meter 75 cm = 1575 cm.
–> 11 meter 25 cm = 1125 cm
–> 7 meter 65 cm = 765 cm.

1575 = 5 * 5 * 3 * 3 * 7
1125 = 5 * 5 * 5 * 3 * 3
765 = 5 * 3 * 3 * 17

HCF of 1575 , 1125 and 765 is 45.

]]> https://www.wikitechy.com/interview-questions/lcm-and-hcf/which-greatest-possible-length-can-be-used-to-measure-exactly-15-meter-75-cm-11-meter-25-cm-and-7-meter-65-cm/feed/ 0 If LCM of two number is 693, HCF of two numbers is 11 and one number is 99, then find other ? https://www.wikitechy.com/interview-questions/lcm-and-hcf/if-lcm-of-two-number-is-693-hcf-of-two-numbers-is-11-and-one-number-is-99-then-find-other/ https://www.wikitechy.com/interview-questions/lcm-and-hcf/if-lcm-of-two-number-is-693-hcf-of-two-numbers-is-11-and-one-number-is-99-then-find-other/#respond Tue, 17 Aug 2021 17:43:48 +0000 https://www.wikitechy.com/interview-questions/?p=1840

If LCM of two number is 693, HCF of two numbers is 11 and one number is 99, then find other ?

A. 12

B. 45

C. 77

D. 34

Answer : C. 77

Explanation:

For any this type of question, remember
Product of two numbers = Product of their HCF and LCM
So Other number = 693 × 11 / 99
= 77

]]> https://www.wikitechy.com/interview-questions/lcm-and-hcf/if-lcm-of-two-number-is-693-hcf-of-two-numbers-is-11-and-one-number-is-99-then-find-other/feed/ 0 The LCM of three different numbers is 1024. Which one of the following can never be there HCF ? https://www.wikitechy.com/interview-questions/lcm-and-hcf/the-lcm-of-three-different-numbers-is-1024-which-one-of-the-following-can-never-be-there-hcf/ https://www.wikitechy.com/interview-questions/lcm-and-hcf/the-lcm-of-three-different-numbers-is-1024-which-one-of-the-following-can-never-be-there-hcf/#respond Tue, 17 Aug 2021 17:41:31 +0000 https://www.wikitechy.com/interview-questions/?p=1839

The LCM of three different numbers is 1024. Which one of the following can never be there HCF ?

A. 8

B. 32

C. 124

D. 256

Answer : C. 124

Explanation:

1024 is dividable by all numbers except 124.

]]> https://www.wikitechy.com/interview-questions/lcm-and-hcf/the-lcm-of-three-different-numbers-is-1024-which-one-of-the-following-can-never-be-there-hcf/feed/ 0 If the sum of two numbers is 55 and the H.C.F. and L.C.M. of these numbers are 5 and 120 respectively, then the sum of the reciprocals of the numbers is equal to ? https://www.wikitechy.com/interview-questions/lcm-and-hcf/if-the-sum-of-two-numbers-is-55-and-the-hcf-and-lcm-of-these-numbers-are-5-and-120-respectively-then-the-sum-of-the-reciprocals-of-the-numbers-is-equal-to/ https://www.wikitechy.com/interview-questions/lcm-and-hcf/if-the-sum-of-two-numbers-is-55-and-the-hcf-and-lcm-of-these-numbers-are-5-and-120-respectively-then-the-sum-of-the-reciprocals-of-the-numbers-is-equal-to/#respond Tue, 17 Aug 2021 17:36:14 +0000 https://www.wikitechy.com/interview-questions/?p=1838

If the sum of two numbers is 55 and the H.C.F. and L.C.M. of these numbers are 5 and 120 respectively, then the sum of the reciprocals of the numbers is equal to ?

A. 11/120

B. 55/501

C. 11/60

D. 12/55

Answer : A. 11/120

Explanation:

Let the numbers be a and b.
Thus a + b = 55 and ab = 5 x 120 = 600
Thus 1/a + 1/b
= (b + a)/(ab)
= 55/600
= 11/120

]]> https://www.wikitechy.com/interview-questions/lcm-and-hcf/if-the-sum-of-two-numbers-is-55-and-the-hcf-and-lcm-of-these-numbers-are-5-and-120-respectively-then-the-sum-of-the-reciprocals-of-the-numbers-is-equal-to/feed/ 0 If A=x3y2 and B=xy3 then find the HCF of A, B ? https://www.wikitechy.com/interview-questions/lcm-and-hcf/if-ax3y2-and-bxy3-then-find-the-hcf-of-a-b/ https://www.wikitechy.com/interview-questions/lcm-and-hcf/if-ax3y2-and-bxy3-then-find-the-hcf-of-a-b/#respond Tue, 17 Aug 2021 17:32:39 +0000 https://www.wikitechy.com/interview-questions/?p=1837

If A=x3y2 and B=xy3 then find the HCF of A, B ?

A. x4y4

B. xy2

C. xy

D. x3

Answer : B. xy2

Explanation:

Given A = x3y2 , B = xy3
A = x*x*x*y*y
B = x*y*y*y
The highest common factor between A and B is xy2.

]]> https://www.wikitechy.com/interview-questions/lcm-and-hcf/if-ax3y2-and-bxy3-then-find-the-hcf-of-a-b/feed/ 0 Find the greatest number that will divide 148 246 and 623 leaving remainders 4 6 and 11 respectively ? https://www.wikitechy.com/interview-questions/lcm-and-hcf/find-the-greatest-number-that-will-divide-148-246-and-623-leaving-remainders-4-6-and-11-respectively/ https://www.wikitechy.com/interview-questions/lcm-and-hcf/find-the-greatest-number-that-will-divide-148-246-and-623-leaving-remainders-4-6-and-11-respectively/#respond Tue, 17 Aug 2021 17:29:52 +0000 https://www.wikitechy.com/interview-questions/?p=1836

Find the greatest number that will divide 148 246 and 623 leaving remainders 4 6 and 11 respectively ?

A. 20

B. 12

C. 6

D. 48

Answer : B. 12…

Explanation:

Remainder in case of 148 = 4
Number = 148 – 4 = 144
Remainder in case of 246 = 6
Number = 246 – 6 = 240
Remainder in case of 623 = 11
Number = 623 – 11 = 612
Now, we have find the H.C.F. of 144, 240 and 612

H.C.F. of 144, 240 and 612 = 2 * 2 * 3 = 12

Therefore, the required number is 12 that will divide 148, 246 and 623 leaving remainders 4, 6 and 11 respectively.

]]> https://www.wikitechy.com/interview-questions/lcm-and-hcf/find-the-greatest-number-that-will-divide-148-246-and-623-leaving-remainders-4-6-and-11-respectively/feed/ 0 The LCM of two positive no’s is 168 and their product is 504. what is the difference in their squares ? https://www.wikitechy.com/interview-questions/lcm-and-hcf/the-lcm-of-two-positive-nos-is-168-and-their-product-is-504-what-is-the-difference-in-their-squares/ https://www.wikitechy.com/interview-questions/lcm-and-hcf/the-lcm-of-two-positive-nos-is-168-and-their-product-is-504-what-is-the-difference-in-their-squares/#respond Tue, 17 Aug 2021 17:26:37 +0000 https://www.wikitechy.com/interview-questions/?p=1835

The LCM of two positive no’s is 168 and their product is 504. what is the difference in their squares?

A. 175

B. 216

C. 9

D. 135

Answer : D. 135…

504 = 2*2*2*3*3*7 = 8*3*3*7 = 24*21
168 = 2*2*2*3*7
It means 3 will come in both the numbers as 3 is coming once in LCM but coming as 9 in product.
so possible numbers are 24 and 21.

Now the difference of the square of these numbers is a^2-b^2 = (a+b)(a-b)
= (24+21)(24-21)
= 45(3)
= 135

]]> https://www.wikitechy.com/interview-questions/lcm-and-hcf/the-lcm-of-two-positive-nos-is-168-and-their-product-is-504-what-is-the-difference-in-their-squares/feed/ 0 Least of number which when divided by 35,45,55 and leaves remainder 18,28,38 is ? https://www.wikitechy.com/interview-questions/lcm-and-hcf/least-of-number-which-when-divided-by-35-45-55-and-leaves-remainder-18-28-38-is/ https://www.wikitechy.com/interview-questions/lcm-and-hcf/least-of-number-which-when-divided-by-35-45-55-and-leaves-remainder-18-28-38-is/#respond Tue, 17 Aug 2021 17:23:05 +0000 https://www.wikitechy.com/interview-questions/?p=1834

Least of number which when divided by 35,45,55 and leaves remainder 18,28,38 is ?

The Difference between any divisor and the corresponding remainder is 17.
Required number= (L.C.M of 35,45,55)-17
= 3465-17
= 3448

]]> https://www.wikitechy.com/interview-questions/lcm-and-hcf/least-of-number-which-when-divided-by-35-45-55-and-leaves-remainder-18-28-38-is/feed/ 0