Question

Find the smallest perfect square number divisible by 12, 15 and 18.

• A. 900
• B. 1600
• C. 400
• D. 100

Answer 1

Answer:

A. 900

Given:

The numbers are 12, 15 and 18.

Concept used:

To make N(LCM) = x^a $\times$ y^b $\times$ z^c perfect square. (where x, y and z are prime numbers and a, b and c are integers)

Multiply the number by the same number whose power is odd.

Calculations:

12 = 2² 4\times 3¹

15 = 3¹ \times 5¹

18 = 2¹ \times 3²

N =  22 \times 3² \times 5¹

Multiply N by 5 to get perfect square,

5N = 22\times$3<span style="color: inherit">2$\times$ 5² = 900

∴ The smallest perfect square number divisible by 12, 15 and 18 is 900.