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The ratio of two numbers is 3 : 5 and their LCM is 105. What is the difference between the numbers?
Question

The ratio of two numbers is 3 : 5 and their LCM is 105. What is the difference between the numbers?

A.

10

B.

7

C.

14

D.

4

Correct option is C

Given:

Ratio of two numbers = 3 : 5

LCM of the numbers = 105

Solution:

Let the numbers be 3x and 5x, where x is a common factor.

The LCM of 3x and 5x is 15x (since 3 and 5 are coprime).

15x = 105

x = 7

First number = 3x = 3×\times7 = 21

Second number = 5x = 5 ×\times​ 7 = 35

Difference = 35 - 21 = 14

The difference between the numbers is 14.

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