Question
The sum and difference of the Least Common Multiple
(L.C.M.) and Highest Common Factor (H.C.F.) of two numbers are 216 and 184, respectively. If one of the numbers is 25, find the other number.Solution
Let the L.C.M and the H.C.F of the two numbers be 'a' and 'b' respectively Then, (a + b) = 216 And (a - b) = 184 So, (a + b) + (a - b) = 216 +184 Or, a = 400 ÷ 2 = 200 So, b = 216 - 200 = 16 The product of two numbers is equal to the product of their L.C.M and H.C.F So, required number = (200 X 16) ÷ 25 = 128
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