Question

The HCF of two numbers is 21 and their sum is 105. The LCM of the numbers is

Answer 1

Let the two no is x and (105- x)
then

x(105-x) = 21 ×LCM
LCM = {x ( 105-x)} / 21

So numbers x and (105-x) has to be multiple of 21 and also the sum is 105
So pairs could be 21, 84 and 42,63 
Accordingly ,
if 21, 84
LCM= (21×84)/21=84 
and for 42 , 63
LCM= (42 × 63)/21= 126

Answer 2

Concept

The product of any two numbers is equal to the product of their HCF and LCM

Given

HCF of two numbers is 21 and their sum is 105

Find

We have to find the LCM of the two numbers

Solution

Let the first number be x

Since the sum of the two numbers is 105, the second number will be (105-x)

We know that

Product of two numbers = LCM* HCF

Thus,

x (105-x) = 21 * LCM

LCM = [x (105-x)]/21

The numbers x and (105-x) have to be such that they are multiples of 21 and also their sum is 105

The only possible pairs are 21, 84 and 42,63

If the numbers are 21 and 84

LCM= (21×84)/21=84

If the numbers are 42 and 63

LCM= (42 × 63)/21= 126

Thus, there are two possible values of the LCM, it can be either 84 or 126

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