The LCM of two numbers is 45 times their $H C F$ . If one of the numbers is 225 and sum of their LCM and $H C F$ is 1150, find the theother number.

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Solution

Let the LCM be $x$
The HCF is $45 \times x = 45 x$
Sum of LCM and HCF $x + 45 x = 1150 46 x = 1150 x = \frac{1150}{46} x = 25$
So LCM is $25$ and HCF is $45 \times 25 = 1125$
Let $a, b$ be two numbers
We know that $a b = L C M \times H C F 225 \times b = 25 \times 1125 b = \frac{28125}{225} b = 125$
So the other number is $125$

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