Question
The sum of the LCM and HCF of two numbers is 370 and the
difference between the LCM and HCF is 354. If one of the numbers is 59, find the other number.Solution
ATQ,
Let the LCM and the HCF of the two numbers be 'a' and 'b', respectively
We have, (a + b) = 370 and (a - b) = 354
So, a + b + (a - b) = 370 + 354
Or, 2a = 724
Or, a = 724 ÷ 2 = 362
So, b = 370 - 362 = 8
We know that product of the two numbers is equal to the product of their LCM and HCF
Let the two numbers be 'x' and 'y' where x = 59
So, 362 × 8 = 59y
So, y = (362 × 8) ÷ 59 = 49
So, the other number is 49
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