Question

What is least number which when divide by 5,6,8,9,12 gives remainder 1in each case is completely divide by 13?

Answer 1

5 = 5
6 = 2 × 3
8 = 2 × 2 × 2 × 2
9 = 3 × 3
12 = 2 × 2 × 3
×××××××××××××
LCM = 5×2×3×2×2×3
LCM = 360

Required number is 360 + 1 = 361

And 361 is not divisible by 13

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Answer 2

Heya !!!

Prime factorisation of 5 = 1 × 5

Prime factorisation of 6 = 2 × 3

Prime factorisation of 8 = 2 × 2 × 2

Prime factorisation of 9 = 3 × 3

And,

Prime factorisation of 12 = 2 × 2 × 3

LCM of 5 , 6 , 8 , 9 and 12 = 2 × 2 × 3 × 5 × 2× 3 = 360

Required number = LCM(5,6,8,9,12) + 1 = 360 + 1 = 361

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