hcf and lcm problems - Wikitechy https://www.wikitechy.com/interview-questions/tag/hcf-and-lcm-problems/ Interview Questions Mon, 20 Sep 2021 04:42:53 +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 hcf and lcm problems - Wikitechy https://www.wikitechy.com/interview-questions/tag/hcf-and-lcm-problems/ 32 32 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 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 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 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 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

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