LCM of two numbers is 22 times their HCF. If one of the numbers is 132 and the sum of LCM and HCF is 276, then what is the other number ?

24

Let us assume HCF be “M”.

According to the question, LCM = 22 M

Sum of LCM and HCF = 276

∴ 22M + M = 276 

M = 13

Substituting the value of M, to find LCM

⇒ LCM = 12 × 22 = 264

Using LCM × HCF = First  number × Second number

⇒ 12 × 264 = 132 × Second number

⇒ Other number = 24