The greatest common multiple of two numbers is 8 while their least common multiple is 144. If one number is 16 then find the other number.

Given: 
GCM or HCF = 8
LCM = 144

Concept: 
L.C.M × H.C.F = Product of two numbers

Calculation:
The first number is 16, let the other number be x.
⇒ L.C.M × H.C.F = 16 × x

⇒ 144 × 8 = 16 × x

⇒ \(x = {144 × 8 \over 16}\)

⇒ \(x = {144 \over 2}\)

⇒ \(x = 72\)

∴ The other number is 72.