If the ratio of two numbers is 2 : 3 and their L.C.M. is

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If the ratio of two numbers is 2 : 3 and their L.C.M. is 54, then the sum of the two numbers is

1. 5
2. 15
3. 45
4. 270

Correct Option: C

Let the two numbers are 2p and 3p respectively.
According to question,
LCM = 54
⇒ p ( 3 × 2 ) = 54
⇒ p = 9
Numbers = 2p = 2 × 9 = 18 and, 3p = 3 × 9 = 27
Sum of the two numbers = 18 + 27 = 45