Question

The lcm of 2 numbers is 14 times their hcf. the sum of lcm and hcf is 600.if one number is 280,then find the other number

Answer 1

Let HCF be 'a' and LCM be 'b'
LCM = 14a
b = 14a -----(1)

Sum of LCM and HCF = 600
b + a = 600
14a + a = 600
15a = 600
a = 600/15
a = 40

HCF of two numbers = 40
LCM of two numbers = 14(40) = 560

We know that,
Product of two numbers = LCM × HCF 
280 × another number = 560 × 40
another number = (560 × 40)/280
another number = 2 × 40 = 80

Therefore,the another number is 80.