Question

Fine the least number which when divided by 12,16,24 and 36 leaves A remainder 10 in each case

Answer 1

$\huge\pink{Answer}$

First of all find LCM and as it leaves remainder of 4 then the number is LCM +4

12=2×2×3=2²×3

16=2×2×2×2=2⁴

18=2×3×3=3²×2

30=2×3×5

LCM (12,16,18,30)=2⁴×3²×5

LCM=16×9×5

LCM=720

The number can be 720+4=724

But the condition is, the number should also be completely divisible by 7

As 724 is not completely divisible by 7

Therefore the number is multiple of 720 plus 4 which is divisible by 7

720×2+4=1444 not divisible by 7

720×3+4=2164 not divisible by 7

720×4+4=2884

2884 is completely divisible by 7

Answer is 2884

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