Question

Two numbers are in the ratio 21 is to 17 if their hcf is 5 find the numbers

Answer 1

$<font color ="blue"/>$

=>let no.=21x and 17x

=>LCM =( 21,17)×x

=>hcf=5

=>lcm×hcf=product

=>5×21x×17x=21x×17x

=>x=5

=>21x=21×5=105

=>17x=17×5=85

=>the numbers are 105 &85

Answer 2

Given:

Two numbers are in the ratio 21: 17. The HCF of the two numbers is 5.

To Find:

The possible numbers satisfying the above conditions are?

Solution:

1. Let the numbers be 21n and 17n.

2. The HCF of the two numbers is 5,

=> The LCM of 21n and 17n will be (21x17)n. (As 17 and 21 are co-primes)

3. The product of LCM and HCF of the two numbers is equal to the product of the two numbers,

=> LCM x HCF = product of the two numbers.

4. Use the above formula to find the numbers,

=> (21x17)n x 5 = 21n x 17n,

=> 5n = n²,

=> n = 5,

5. Hence the numbers are 17x5, 21x5.

=> The numbers are 85 and 105.

Therefore, the numbers are 85 and 105.