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Theory

    ➡ Product of two numbers = Product of their LCM and HCF

The highest common factor(HCF) and the least common multiple(LCM) of two positive integers are 7 and 140

HCF = 7, LCM = 140 = 7 * 2 * 2* 5

The numbers are between 20 and 45 and we need to find the sum of both the numbers.

Now, we can start taking numbers such that the two numbers are a multiple of the HCF, which is 7, and their LCM = 140

1. We can take one number as 7*1, and other as 140 to have HCF = 7 and LCM=140, but the two numbers won't be between 20 and 45 then => NOT POSSIBLE

2. We can take one number as 7*2, and other as 140 to have HCF = 7 and LCM=140, but the two numbers won't be between 20 and 45 then => NOT POSSIBLE

3. We can take one number as 7*2*2, and other as 7*5 to have HCF = 7 and LCM=140, making the two numbers as 28 and 35. Both the numbers are within 20 and 45 => POSSIBLE

Sum of the numbers = 28 + 35 = 63

So, Answer will be C.
Hope it helps!

Watch the following video to Learn the Basics of LCM and GCD

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