Question

the L.C.M.of two numbers is 48.the numbers ares in the ratio 2:3.then sum of the numbers is:

Answer 1

For 48 to be an LCM (lowest common multiple), then the factors of 48 are what you need to look at. 1,2,3,4,6,8,12,16,24,48. Easily found by pairing off the small integers with their corresponding factor, 1x48, 2x24, 3x16 etc.

Alternatively, you can solve this in a more general way. For the ratio to be 2:3 there is a factor of 6 (the LCM of 2 and 3), so the HCF for this problem will be 48/6 = 8. That can be seen by looking back at your definition of LCM, which (in my teaching, anyway), is that LCM(a,b) = a*b / HCF(a,b). Note that this method does not directly declare 16 and 24 as an intermediate answer.