Question

Lcm of two numbers is 40 times their hcf . the sum of the lcm and hcf is 1476. if one of the numbers is 288, find the other numbers

Answer 1

Answer:  The other number is 180.

Step-by-step explanation:  Given that the lcm of two numbers is 40 times their hcf and the sum of the lcm and hcf is 1476.

One of the numbers is 288.

We are to find the other number.

Let x be the other number and h be the hcf of x and 288.

Then, lcm = 40h.

We know that the product of any two numbers is equal to the product of their hcf and lcm.

So, we get

$x\times288=h\times40h\\\\\Rightarrow x=\dfrac{40h^2}{288}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

Also,

$h+40h=1476\\\\\Rightarrow 41h=1476\\\\\Rightarrow h=\dfrac{1476}{41}\\\\\Rightarrow h=36.$

From equation (i), we get

$x=\dfrac{40}{288}\times36^2=40\times4.5=180.$

Therefore, the other number is 180.