Question

Find the smallest number which when increased by $15$ is exactly divisible by $468$ and $520$

Answer 1

Step 1 : Find the LCM of both the numbers $468$ and $520$

$2$	$468,520$
$2$	$234,260$
$13$	$117,130$
	$9,10$

$LCM=2\times 2\times 13\times 9\times 10=4680$

Now, $4680$ is divisible by both $468$ and $520$

we need to find the number which when increased by $15$ is exactly divisible by $468$ and $520$

Step 2 : So we subtract $15$ from the LCM of $468$ and $520$ which is $4680$.

$4680-15=4665$

Hence, the smallest number which when increased by $15$ is exactly divisible by $468$ and $520$ is $4665$