The HCF of two numbers is 145 and their LCM is 2175. If one of the numbers is 725, Find the other number.

The largest possible number which divides the given numbers exactly without leaving any remainder is called the HCF (Highest Common Factor).

Answer: The other number is 435

The Least Common Multiple (LCM) of two numbers a and b is the smallest number which is divisible by a and b exactly.

Explanation:

The formula that shows the relation between LCM and HCF of a and b is: LCM (a,b) = (a × b) / HCF (a,b)

One number is a = 725

HCF (725, b) is 145, and LCM (725, b) = 2175

LCM (725, b) = (725 × b) / HCF (725, b)

2175 = (725 × b) / 145

725 × b = 2175 × 145

b = 315375/725

= 435

Therefore, the other number is 435.