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Question

The least number which when divided by $9, 12, 16, 30$ leaves in each case a remainder of $3$ is
$720$
$723$
$823$
$750$

A

823

B

750

C

720

D

723

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Solution

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$9 = 3 \times 3$
$12 = 3 \times 2 \times 2$
$16 = 2 \times 2 \times 2 \times 2$
$30 = 3 \times 5 \times 2$
LCM = $2 \times 3 \times 2 \times 3 \times 1 \times 4 \times 5 = 720$
$∴$ required number $= 720 + 3 = 723$

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