LCM-algebraic method-eighth grade

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Problem: The L.C.M. of two numbers is 48, and the numbers are in the ratio of 2:3. Find the numbers.

Solution: Let the two numbers be 2x and 3x. Therefore, LCM = 6x

Their HCF = x

The product of the two numbers = HCF X LCM

i.e., 2x X 3x = x X 48

i.e., 6x = 48

Therefore, x = 8

Hence, the numbers are 8 X 2 and 8 X 3, i.e., 16 and 24.