On sports day, three students run round a circular track. One round takes them 36 seconds, 48 seconds and 60 seconds. They start together from the same point. After how much time will they next meet at the starting point?

1. 1 · Write what is given and what is to be found. Times for one round: 36 s, 48 s and 60 s. To find: the first time all three are back at the start together.
2. 2 · Decide: HCF or LCM. Each runner is at the start only after whole rounds. So the time is a common multiple of 36, 48 and 60. The first such time is the LCM.
3. 3 · Write the method. LCM = product of the greatest power of each prime.
4. 4 · Factorise. 36 = 2² × 3², 48 = 2⁴ × 3, 60 = 2² × 3 × 5
5. 5 · Find the LCM. LCM = 2⁴ × 3² × 5 = 16 × 9 × 5 = 720 seconds
6. 6 · Say what it means. 720 seconds = 12 minutes. By then they have run 20, 15 and 12 rounds.
7. 7 · Check and box the answer. 720 ÷ 36 = 20, 720 ÷ 48 = 15, 720 ÷ 60 = 12. Therefore they meet again after 720 seconds, that is 12 minutes.

Scoring tip: Write one line saying why you chose the LCM. Examiners give credit for the reason, not just the number.