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Question 104
L.C.M. of two numbers is 120 and their H.C.F. is 10. Which of the following can be the sum of those two numbers?
Solution
We assume that numbers are $$hr_1$$ and $$hr_2$$ (where h= H.C.F. of numbers and $$r_1$$Â and $$r_2$$ are prime factors)
So L.C.M. will be = $$hr_1r_2$$ = 120
or $$r_1r_2$$ = 12
So $$r_1$$ =4 and $$r_2$$ = 3 ; numbers will be 40 and 30, sum is 70
or $$r_1$$ = 12 and $$r_2$$ = 1 ; numbers will be 120 and 10, sum is 130
Hence only option D justifies.
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