Question

Three numbers are in the ratio 3 : 5 : 7 and their LCM is 2520. Their HCF is​

Answer 1

Answer:

Let us consider the number be 3x,7x and 5x

The L.C.M of the three numbers be =105x

105x = 2520

x = 2520/105

x = 24

Then the number be

3x = 3 × 24 = 72

4x = 7 × 24 = 168

5x = 5 × 24 = 96

∴ The HCF of the three numbers be 24.

Answer 2

To find : HCF of given numbers .

Given : LCM = $2520$  , numbers in ratio = $3 : 5 : 7$

Solution :

• Let , three numbers in ratio be $3x , 5x , 7x$ . We are given that LCM of three numbers is $2520$ .  
• LCM of three numbers = $105x$
• Therefore,

                      $105x = 2520 \\x = \frac{2520}{105} \\x = 24$

• Now , numbers are :

           $3x = 3\times 24= 72 \\5x = 5\times 24= 120\\7x = 7\times 24 = 168$

• To find HCF of $72,120, 168$  we find factors of these numbers .
• Prime Factors are:
• $72 = 2\times 2\times 2\times 3\times 3$
• $120 = 2\times 2\times 2\times 3\times 5$
• $168 = 2\times 2\times 2\times 3\times 7$
• HCF = $2\times 2\times 2\times 3$

                $= 24$

Hence , HCF of $72,120, 168$ is $24$ .