Question
The sum and the difference of the
L.C.M and H.C.F of two numbers are 486 and 342. If one of the numbers is 18, 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) = 486
And (a - b) = 342
So, (a + b) + (a - b) = 486 + 342 = 828
Or, a = 828 ÷ 2 = 414
So, b = 486 - 414 = 72
The product of two numbers is equal to the product of their L.C.M and H.C.FSo, required number = (414 × 72) ÷ 18 = 1656
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