Question

Two numbers are in the ratio 2 ratio 3 and lcm is 48. sum of the numbers is?

Answer 1

Let the numbers be 2x and 3x.
Then, their L.C.M. = 6x. 
So, 6x = 48 or x = 8.
∴ The numbers are 16 and 24.
Hence, required sum = (16 + 24) = 40.

Answer 2

The sum of the number is 40

Explanation:

Given:

1. Two numbers are in the ratio 2:3

2. lcm is 48.

To find:

The sum of the numbers

Least Common Multiple:

LCM of two or more numbers is the smallest number, which is exactly divisible by each of the given numbers.

Formula:

LCM of the numbers = Product of the numbers

Solution:

==>  LCM = 48

==> Two numbers = 2:3

==> Two numbers are a and b

==> a = 2x

==> b = 3x

==> LCM of 2 and 3 is 6

==> LCM of two numbers = 6x

==> LCM of the numbers = Product of the numbers

==> 48 = 6x

==> x = 48÷6

==> x=8

==> a = 2(8)

==> a = 16

==> b = 3(8)

==> b = 24

==> Two numbers are 16 and 24

==> Sum of the numbers = a+b

==> a+b = 16+24

==> Sum of the numbers = 40

==> The sum of the number is 40