Question

LCM of two numbers is 45 times their HCF if one of the numbers is 125 and sum of their HCF and LCM is 1150 find the other number

Answer 1

Let the lcm be x and hcf be y and the other number be z.

Given lcm of 2 numbers is 45 times their hcf, the sum of HCF + LCM is 1150.

y = 45x. ---- (1)

x + y = 1150   --- (2)


Substitute equation (1) in (2), we get

46x = 1150

x = 25.


Substitute x = 25 in (1), we get

y = 45 * 25 = 1125.


We know that  product of two numbers = LCM * HCF

                                125 * z = 25 * 1125

                                z = 25 * 1125/125

                                   = 225.


The other number = 225.

Answer 2

Answer: Let the lcm be x and hcf be y and the other number be z.

Given lcm of 2 numbers is 45 times their hcf, the sum of HCF + LCM is 1150.

y = 45x. ---- (1)

x + y = 1150   --- (2)

Substitute equation (1) in (2), we get

46x = 1150

x = 25.

Substitute x = 25 in (1), we get

y = 45 * 25 = 1125.

We know that  product of two numbers = LCM * HCF

                               125 * z = 25 * 1125

                               z = 25 * 1125/125

                                  = 225.

The other number = 225.

hope it helps.....