Question

The hcf of two numbers is 9.their lcm is 252.find their sum?

Answer 1

answer : 99 and 261

Let two numbers are ‘a’ and ‘b’

a/c to question,

HCF of a and b = 9

and we know, HCF means highest common factor of two numbers.

e.g., 9 is the highest common factor of a and b.

so, we can write a = 9k and b = 9l , where k and l are co-prime numbers.

again, LCM of a and b = 252

or, LCM of 9k and 9l = 252

or, 9 × k × l = 252

or, k × l = 28

case 1 : if k = 4 then, l = 7 or if k = 7 then, l = 4

Let's take k = 4 and l = 7

then, a = 9k = 36 and b = 9l = 63

hence, sum of numbers = 36 + 63 = 99

case 2 : if k = 1 then, l = 28 or if k = 28 then, l = 1

Let's take k = 1 and l = 28

then, a = 9k = 9 and b = 9l = 252

hence, sum of numbers = 9 + 252 = 261

hence, there are two possible answers e.g., 99 and 261.

Answer 2

Answer:

I step: LCM/ HCF = 252/9 = 28

II step : 28 = 1 x 28; 2 x 14; 4 x 7.

So we got 3 pairs of factors.

1 x 9, 28 x 9 ; 2 x 9, 14 x 9 ; 4 x 9, 7 x 9.

the two numbers are 9 and 252 or 36 and 63.

The sum of the two numbers can be 9+252 = 261 or 36+63 = 99.

Step-by-step explanation: