The highest common factor of 108, 72 and 5a is a. What can be the least common multiple of 108, 72 and a?
Answer & explanation
Correct answer: option 4
HCF of 108, 72 and 5a = a
⇒ 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