Question

Find the smallest number which when increased by $17$ is exactly divisible by $520$ and $468$.

Answer 1

Step 1: Find the LCM

Given numbers are $468$ and $520$

Prime factors of $468$ are

$468=2\times 2\times 3\times 3\times 13$

Prime factors of $520$ are

$520=2\times 2\times 2\times 5\times 13$

$\therefore$LCM of $468$ and $520$ is

LCM$\left(468,520\right)=2\times 2\times 2\times 3\times 3\times 13\times 5=4680$

Step 2: Find the smallest number

As per given condition, the number increased by $17$ is exactly divisible by $520$ and $468$

$\therefore 4680-17=4663$

Hence, the number is $4663$.