Question
The sum and difference of the L.C.M and H.C.F of two
numbers are 540 and 300. If one number is 60, find the other.Solution
ATQ,
Let the L.C.M and the H.C.F of the two numbers be 'a' and 'b' respectively
Then, (a + b) = 540
And (a - b) = 300
So, (a + b) + (a - b) = 540 + 300 = 840
Or, a = 840 ÷ 2 = 420
So, b = 540 - 420 = 120
The product of two numbers is equal to the product of their L.C.M and H.C.FSo, required number = (420 × 120) ÷ 60 = 840
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