Question
The square of sum of two numbers is 36,864 and the sum
of squares of the same two numbers is 21,024. If their H.C.F. is 12, then find their L.C.M.ÂSolution
Let the two numbers be 'a' and 'b'
We have, (a + b) ² = 36864
And, a² + b² = 21024
(a + b) ² = a² + b² + 2ab = 21024 + 2ab
Or, 2ab = 36864 – 21024 = 15840
So, ab = 15840/2 = 7920
Therefore, L.C.M = 7920 / 12 = 660
Hence, option A.
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