Question

the lcm of two numbers is 48 and the numbers are in the ratio 2:3.the sum of the numbers =?

Answer 1

Let the numbers be 2x and 3x

We will find the LCM of 2x and 3x

2x = 2 × 1 × x

3x = 3 × 1 × x

LCM = 2 × 3

= 6

LCM = 6x

But their LCM is given 48

=> 6x = 48

=> x = $\frac{48}{6}$

=> x = 8

So, the numbers are 2 × 8 i.e 16 & 3 × 8 i.e 24


Hence the sum of numbers = 16 + 24 =40

Answer 2

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Let,
The numbers be 2x and 3x

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We will find the LCM of 2x and 3x 

2x = 2 × 1 × x

3x = 3 × 1 × x

LCM = 2 × 3 

= 6

LCM = 6x 

But their LCM is given 48

➡6x = 48

➡ x =8

So, the numbers are 2 × 8 i.e 16 & 3 × 8 i.e 24

Hence,
the sum of numbers = 16 + 24 =40