Question

Tom and David get their hair cut at the Broadway Barber Shop on Saturdays. Tom gets his hair cut every 4 weeks. David gets his hair cut every 6 weeks. One Saturday, Tom and David got their hair cut at the same time. When will Tom and David get their hair cut on the same day again?Tom and David will get their hair cut on the same day in weeks.

(a) 2 weeks
(b) 8 weeks
(c) 12 weeks
(d) 24 weeks

Answer 1

I made a chart listing 4 and 6, but you keep adding 4 and 6 until you find a common number. In this case it’s 12. So the answer is C 12 weeks

Answer 2

To determine when Tom and David will get their hair cut on the same day again, we find the Least Common Multiple (LCM) of their haircut frequencies. The LCM of 4 and 6 is 12, so they will next have their hair cut on the same day in 12 weeks (c).

Step-by-step explanation:

The question involves finding a common multiple, which in this context is the least number of weeks after which both Tom and David will get their hair cut on the same day again.

Since Tom gets his hair cut every 4 weeks and David every 6 weeks, we need to find the Least Common Multiple (LCM) of 4 and 6. The multiples of 4 are 4, 8, 12, 16, 20, 24, and so on, while the multiples of 6 are 6, 12, 18, 24, and so on. The first common multiple is 12, which means they will both get their hair cuts again on the same day in 12 weeks.

Therefore, the correct answer is (c) 12 weeks. This is an example of a real-life application of LCM in scheduling.