Question

The l.c.m and h.c.f of two numbers is 9 times their HCF. The sum of LCM and HCF is 500. Find the HCF of two numbers.​

Answer 1

50

Explanation:

There are 2 prime factors that are different and 2 numbers that we look for that are identical when looking for prime factors.

So for numbers that don't end in 0 like 500 we can start with 3 to get 27 as one of the two numbers, then we look to see if 27 divides into that.

But for 500 it will always be numbers that end in 0 or 5 and also 1, 2 and 4

So we work with 9+1 = 10

x = 10

500/10 = 50

Answer 2

Correct question:

The LCM of two numbers is 9 times their HCF .The sum of LCM and HCF is 500 . Find the HCF​ of two numbers.​

Answer:

The HCF of two numbers is 50.

Explanation:

let the H.C.F of the two numbers = x

let the L.C.M of the two numbers = y

y = 9x -------equation (1)

y + x = 500 -------- equation (2)

y = 500 - x

Substitute in the value of y in equation (1)

500 - x = 9x

500 = 9x + x

500 = 10x

x = 500 / 10

x = 50

Therefore, the HCF of two numbers is 50.