Three bells toll together at intervals of $9, 12, 15$ minutes respectively. If they toll together now, after how much time will they toll together next?
$180$ minutes
$90$ minutes
$360$ minutes
$45$ minutes
Step-by-Step Solution
Key Concept: Required time is $\text{LCM}(9, 12, 15)$.
Stepwise Solution:
$9 = 3^2, 12 = 2^2 \times 3, 15 = 3 \times 5$. [0.5 Mark]
$\text{LCM}(9, 12, 15) = 2^2 \times 3^2 \times 5 = 4 \times 9 \times 5 = 180$ minutes. [0.5 Mark]
Marking Scheme:
• Prime factorisations: 0.5 Mark
• LCM $= 180$ minutes: 0.5 Mark
Correct Answer: $180$ minutes