Question

Find the least number of five digits which is exactly divisible by each of 32, 36, 60, 90 and 144.​

Answer 1

The least number that is divisible by 32, 36, 60, 90 and 144 is it's LCM

LCM of 32, 36, 60, 90, 144 is

32 = 2^5

36 = 2²×3²

60 = 2×3×5

90= 2×3²×5

144 = 2⁴×3²

LCM = 2^5 × 3² × 5

= 32×9×5

= 1440

Therefore, the smallest 5 digit number that is divisible by 32, 36, 60, 90, 144 is

1440 × 7 = 10080

(1440×6=8640 which is only 4 digits)

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