LCM of two numbers is 56 times their HCF, with the sum of their HCF and LCM being 1710. If one of the two numbers is 240, then what is the other number?

210

LCM = 56 × HCF

HCF + LCM = 1710

Let, HCF = x and LCM = 56x

So, x + 56x = 1710

⇒ 57x = 1710

⇒ x = \(\frac{1710}{57}\) = 30

Then, HCF = 30 and LCM = 30 × 56 = 1680

One number = 240

Let, another number = y

Therefore, 30 × 1680 = 240 × y

⇒ y = \(\frac{30 × 1680}{240}\) = 210