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Question

Find the least number which when divided by 6,15 and 18 leave remainder 5 in each case.


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Solution

Solve for the required number

Given numbers are: 6,15 and 18.

Prime factorisation of given numbers is

6=2×315=3×518=2×3×3

LCM6,15,18=2×3×3×5=90

The number that is 5 more than their LCM will leave a remainder of 5 when divided by the given numbers. Thus, the required number is,

5+90=95.

Therefore, when the number 95 when divided by 6,15 and 18, will leave a remainder of 5.


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