The highest common factor of 108, 72 and 5a is a. What can be the least common multiple of 108, 72 and a

The highest common factor of 108, 72 and 5a is a. What can be the least common multiple of 108, 72 and a?

a) 108

b) 216

c) 72

d) 36

Sol:

Given: 

HCF of 108, 72 and 5a = a 

Calculation: 

⇒ 108 = 72 × 1 + 36 

⇒ 72 = 36 × 2 + 0 

⇒ Third number = 5a = 5 × 36 = 180

 ⇒ Now, we got a = 36 

⇒ 108 = 2 × 2 × 3 × 3 × 3 

⇒ 72 = 2 × 2 × 2 × 3 × 3 

⇒ 36 = 2 × 2 × 3 × 3 

⇒ LCM of 108, 72 and 36 = 2 × 2 × 3 × 3 × 3 × 2 = 216

 Therefore, the LCM of 108, 72 and a is 216, where a is 36.