Question
The L.C.M and H.C.F of two numbers have a sum and
difference of 440 and 120. If one number is 40, 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) = 440
And (a - b) = 120
So, (a + b) + (a - b) = 440 + 120 = 560
Or, a = 560 ÷ 2 = 280
So, b = 440 - 280 = 160
The product of two numbers is equal to the product of their L.C.M and H.C.FSo, required number = (280 × 160) ÷ 40 = 1120
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