Discussion

The least square number which is exactly divisible by 10, 12, 15 and 18, is:

Answer: B

The least square number divisible by 10, 12, 15 and 18 is 900.

Any number divisible by all four is a multiple of their LCM. A square must have every prime factor to an even power.

\[ \begin{aligned} \text{LCM} &= 2^2 \times 3^2 \times 5 = 180 \\ \text{square} &= 180 \times 5 = 900 = 30^2 \end{aligned} \]

Only the 5 has an odd power in 180, so one more 5 makes the smallest square multiple.

400 and 1600 are squares but are not divisible by 3, so they fail 12, 15 and 18. 729 is \(27^2\) but it is odd, so it is not divisible by 10 or 12.

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