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