Question
The sum and difference of L.C.M and H.C.F of two numbers is
312 and 208 respectively. If one of the numbers is 52, find the other number.Solution
ATQ,
Let the L.C.M and the H.C.F of the two numbers be 'a' and 'b' respectively
Then, (a + b) = 312
And (a - b) = 208
So, (a + b) + (a - b) = 312 + 208 = 520
Or, a = 520 ÷ 2 = 260
So, b = 312 - 260 = 52
The product of two numbers is equal to the product of their L.C.M and H.C.FSo, required number = (260 × 52) ÷ 52 = 260
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