Question

The H.C.F of 2 nos, is 1/28 of their L.C.M and the sum of the L.C.M and the H.C.F is 116.If one of the numbers is 1`6, find the other?

Answer 1

Other number is `28`

Explanation:

Let HCF of two numbers say `16` and `b` be `H` and their LCM be `L`

Hence `H/L=1/28` (i.e. `L=28H` and `H+L=116` also `HxxL=16b`

Hence `H+28H=116`

i.e. `29H=116` and `H=116/29=4`

and `L=28xx4=112`

and we have `4xx112=16xxb`

i.e. `b=(4xx112)/16=28`