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Question

Determine the smallest natural number , which when divided by 12,16,24 leaves remainder 7 in each case.


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Solution

Explanation:

To find the number divisible by 12,16,24 , we have to find the LCM.

12=2×2×316=2×2×2×224=2×2×2×3

The LCM =2×2×2×2×3=48

From given information, The number leaves a remainder of 7

So,the smallest natural number =48+7=55

Hence,the smallest number divisible by 12,16,24 leaves a remainder 7 will be 55.


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