If a is an odd number, b is not divisible by 3 and LCM of . . .

Question : If a is an odd number, b is not divisible by 3 and LCM of a and b is P, then LCM if 3a and 2b is 

a) 3P

b) 2P

c) 6P

d) 8P

Doubt by Zoha

Solution : 

a is an odd number (Given)

⇒ a is not divisible by 2.

b is not divisible by 3. (Given)

LCM (a,b) = P (Given)

3a = 3×a
2b = 2×b

LCM (3a,2b) = LCM (3,2) × LCM (a,b)
LCM (3a,2b) = 6 × P
LCM (3a,2b) = 6P

so, LCM of 3a and 2b is 6P.

Hence, c) would be the correct option.