Question
The square of sum of two numbers is 25,600 and the sum
of squares of the same two numbers is 13,000. If their H.C.F. is 10, then find their L.C.M.Solution
Let the two numbers be 'a' and 'b'
We have, (a + b) ² = 25600
And, a² + b² = 13000
(a + b) ² = a² + b² + 2ab = 13000 + 2ab
Or, 2ab = 25600 - 13000 = 12600
So, ab = 12600/2 = 6300
Therefore, L.C.M = 6300 / 10 = 630
Hence, option C.
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