Find the least common multiple of 18, 24, and 30.

hard 3 marks Class 5 · Mathematics · Be My Multiple I Will Be Your Factor

Answer

360

The correct answer is 360 — Multiply these highest powers: $2^{3} \times 3^{2} \times 5 = 8 \times 9 \times 5 = 72 \times 5 = 360$ .

Step-by-step solution

Prime factorise each number: $18 = 2 \times 3^{2}$ , $24 = 2^{3} \times 3$ , $30 = 2 \times 3 \times 5$ .
For each prime take the greatest exponent present: $2^{3}$ (from 24), $3^{2}$ (from 18), and $5$ (from 30).
Multiply these highest powers: $2^{3} \times 3^{2} \times 5 = 8 \times 9 \times 5 = 72 \times 5 = 360$ .

Common mistake: Adding the highest exponents instead of multiplying them

Concept tested: Least common multiple of three numbers