Question
The total and the difference of L.C.M and H.C.F of two
numbers is 378 and 126. If one of the numbers is 27, what is 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) = 378
And (a - b) = 126
So, (a + b) + (a - b) = 378 + 126 = 504
Or, a = 504 ÷ 2 = 252
So, b = 378 - 252 = 126
The product of two numbers is equal to the product of their L.C.M and H.C.FSo, required number = (252 × 126) ÷ 27 = 1176
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