Math, asked by ppsssahith, 8 months ago

The H.C.F. and L.C.M. of two numbers are 24 and 1008 respectively. If one of the two numbers is 168, find the other number.

Answers

Answered by prekshitchauhan22
10

Answer:

The question hinges on the idea that for two numbers a and b, HCF(a, b) × LCM(a, b) = a×b. Here, HCF = 36 and LCM = 1008, so HCF×LCM = 36288. Now, we know one of the numbers (call it “a”) is 144, so 144×b = 36288, which means b = 252. You can check to make sure this is right; is 36 really the HCF? Well, 144 = 4*36, and 252 = 7*36, and since 4 and 7 have no factors in common, 36 has to be the largest number that is a common factor of both, so that's right. That should automatically mean 1008 is the LCM, and it is.

So, the other number is 252.

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