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LCM of two numbers is 120 and their HCF is 10. Which of the following may be equal to the sum of those two numbers?
1. 140
2. 80
3. 60
4. 70

1 Answer

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Best answer
Correct Answer - Option 4 : 70

Concept

HCF : The greatest common divisor of two or more positive integers happens to be the largest positive integer that divides the numbers without leaving a remainder.
LCM : The Least common multiple or lowest common multiple, or smallest common multiple of two integers a and b, usually denoted by l.c.m.(a, b), is the smallest positive integer that is divisible by both a and b.

Co-prime : Two numbers are co-prime if they no common factor other than 1.

Formula used

Product of numbers = LCM × HCF

Calculation

HCF = 10

So, let the two numbers be 10a and 10b, where 'a' and 'b' are co-primes 
LCM of two numbers = 120

⇒ 10a × 10b = LCM × HCF

⇒ 100 ab = 1200

⇒ ab = 12
Therefore, possible pairs of a and b could be 
(3,4)

So, the numbers are (30, 40)
Hence, their sum is 70.

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