The LCM of two numbers is 84. If the numbers are in the ratio2:3, then find the sum of the numbers.

Correct option is B

Given:

​LCM of two numbers is 84

Numbers are in the ratio 2:3

Formula used:

LCM (a, b) = $$\frac{a\times b}{GCD(a,b)}$$ 

Solution:

Let the two numbers be a and b. Since the numbers are in the ratio 2 : 3, we can express them as:

a = 2k  and b = 3k the

LCM is 84. So,

LCM(2k,3k) = 84

​$$\frac{(2k)\times(3k)}{k} = 84$$

$$\frac{6k^2}{k}= 84$$​​​

6k = 84

k = 14

substitute k = 14 into the expression for a and b 

a = 2k = 2 × 14 = 28

b = 3k = 3 × 14 = 42

The sum of the numbers a and b is 

28 + 42=70

The sum of the numbers is 70.

Thus, correct option is (b)

aa BBBis:

​