Question
The square of sum of two numbers is 4,096 and the sum of
squares of the same two numbers is 2,176. If their H.C.F. is 8, then find their L.C.M.Solution
Let the two numbers be 'a' and 'b'
We have, (a + b)² = 4096
And, a² + b² = 2176
(a + b) ² = a² + b² + 2ab = 2176 + 2ab
Or, 2ab = 4096 - 2176 = 1920
So, ab = 1920/2 = 960
Since product of two numbers = L.C.M × H.C.F.
Therefore, L.C.M = 960 / 8 = 120
Hence, option C.
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