Question

UMOJA

Find the greatest number of six digits which is exactly divisible by 27, 45, 60, 72 and 96.

Answer 1

Answer:

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Answer 2

Answer:

To find the largest 6 digit multiple of these numbers, we can find the LCM of these numbers, and the required number will be a multiple of the LCM

So,

27 = 3 x 3 x 3

45 = 3 x 5 x 3

60 = 3 x 4 x 5

72 = 3 x 3 x 2 x 2 x 2

96 = 3 x 2 x 2 x 2 x 2 x 2

so LCM = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 5

LCM = 4320

To find largest 6 digit multiple of 4320, we divide 4320 by largest 6 digit number i.e. 999999, we get

999999 / 4320 = 231.48

So, largest multiple will be 4320 x 231 = 997920