Question

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.

Answer 1

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.