Q. Find out the smallest 5-digit number which is completely divisible by 12, 24, 36 and 64.

10368

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10386

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10000

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10576

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Solution

The correct option is A 10368
LCM of 12, 24, 36 and 64

$12 = 2^{2} \times 3; 24 = 2^{3} \times 3; 36 = 2^{2} \times 3^{2}; 64 = 2^{6}$

$L C M = 2^{6} \times 3^{2} = 64 \times 9 = 576$

$S m a l l e s t 5 - d i g i t n u m b e r = 10000$

$N o w, 10000 / 576 \to R e m a i n d e r = 208$

$D e s i r e d n u m b e r = 10000 + (576 - 208)$

$= 10000 + 368 = 10368.$

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