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What is the least number of five digits which is exactly divisible by 8, 12, 18, 40 and 45?

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10080

10000

10808

10800

answer is A.

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Detailed Solution

We have been given the numbers 8, 12, 18, 40 and 45.
We know, the smallest five-digit number is 10000.
Prime factors of 8, 18, 40 and 45,

8 = 1 × 2 × 2 × 2 = 23

12 = 1 \times 2 \times 2 \times 3 = 2^{2} \times 3^{1}

18 = 1 × 2 × 3 × 3 = 21 × 32

40 = 1 × 2 × 2 × 2 × 5 = 23 × 51

45 = 1 × 3 × 3 × 5 = 32 × 51

Now, the LCM of 8, 12, 18, 40 and 45,

23 × 32 × 51 = 360

On dividing 10000 by 360, we get 27.78 as the quotient.
The integer that is just greater than 27.78 is 28.
Multiplying 360 and 28 to get the required value,

360 × 28 = 10080

Therefore, the required number is 10080.
Hence, option 1 is correct.

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