Find the smallest number which when increased by 17 is exactly di… - Vidyadip

Question

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

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Answer

The smallest number which when increased by $17$ is exactly divisible by both $520$ and $468$ is obtained by subtracting $17$ from the $LCM$ of $520$ and $468$
$468 = 2^2 \times 3^2 \times 13$
$520 = 2^3 \times 5 \times 13$
$LCM = 2^3 \times 3^2 \times 5 \times 13$
$= 4680$
Smallest number which when increased by $17$ is exactly divisible by both $520$ and $468 = 4680 - 17 = 4663$

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