If the ratio of two numbers is 3 : 4 and their LCM is 72, then the sum of the two numbers is:

Correct option is D

Given:

Ratio of two numbers = 3 : 4

LCM of the two numbers = 72

Need: Sum of the two numbers

Formula Used:

LCM =$$\frac{\text{Product of numbers}}{\text{HCF}}$$​

Solution:

Assume numbers

Numbers = 3k, 4k

LCM of 3k and 4k =$$\frac{3k \times 4k}{\gcd(3k,4k)}$$​​

So,

LCM =$$\frac{12k^2}{k}$$​= 12k

Equating with given LCM

12k = 72

k = 6

numbers are:

3k = 18, 4k = 24

Sum of numbers

18 + 24 = 42