The LCM of two numbers is 14 times their HCF. The sum of LCM and HCF is 600. If one number is 280, then find the other number.

LCM of the two numbers a and b is the least number which is exactly divisible by both the numbers a and b.

Answer: The other number is 80

The relation between LCM (Least Common Multiple) and HCF (Highest Common Factor) of two numbers a and b is given by the formula, LCM (a,b) = (a × b) / HCF (a,b)

Explanation:

Let's assume the LCM and HCF of the two numbers are 'x' and 'y' respectively.

Then, x = 14y, and x + y = 600

Substitute x = 14y in the equation x + y = 600 and find the values of 'y'.

x + y = 600

14y + y = 600

15y = 600

y = 600/15

y = 40

Now substitute y = 40 in equation x = 14y and find the value of 'x'

x = 14y

x = 14 × 40

x = 560

Therefore, the LCM and HCF of the two numbers are 560 and 40 respectively.

Now use the formula LCM (a,b) = (a × b) / HCF (a,b) and substitute a = 280, 560 for LCM(a, 280) and 40 for HCF(a, 280), to calculate the another number 'a'

LCM (a,b) = (a × b) / HCF (a,b)

560 = (a × 280) / 40

560 = a × 7

a = 560/7

a = 80

Thus, the other number is 80.