Find the least number which when divided by 8 12 16 and 24 leaves in each case the same remainder 5

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Solution

Step 1: Firstly the LCM of $8, 12, 16, 24 .$
$8 = 2 x 2 x 2 12 = 2 x 2 x 3 16 = 2 x 2 x 2 x 2 24 = 2 x 2 x 2 x 3$
Step 2: LCM of $8, 12, 16, 24 = 2 x 2 x 2 x 2 x 3 = 48$
Step 3: The required no divided by $8, 12, 16, 24$ gives the remainder is $5 .$
Therefore the required no is $48 + 5 = 53 .$
Least number which when divided by $8 12 16 and 24$ leaves in each case is $53$

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