Question

Hcf of two numbers is 17. if the numbers are in the ratio 3:7, then their lcm is?

Answer 1

two numbers are 3×17 =51 &7×17 =119
lcm of 51 &119 is 3×7×17=357

Answer 2

Their LCM is 357

Given : HCF of two numbers is 17. The numbers are in the ratio 3:7

To find : The LCM of the two numbers.

Solution:

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to calculate the value of LCM)

Let, the numbers = 3x and 7x

(Obtained from the ratio 3:7)

Their HCF :

• 3x = 3 × x
• 7x = 7 × x
• common factor = x
• HCF = x

According to the data mentioned in the question,

x = 17

First number = 3x = 3 × 17 = 51

Second number = 7x = 7 × 17 = 119

Here, we will be using the following mathematical relationship.

Product of two numbers = LCM of two numbers × HCF of two numbers

So, by putting the available data :

(51 × 119) = 17 × LCM of two numbers

LCM of two numbers = (51 × 119)/17 = 357

(This will be considered as the final result.)

Hence, the LCM of two numbers is 357