Question

Tom and David get their haircut at the barber shop on Saturdays.Tom gets his hair cut every 3 weeks. David gets his hair cut every 4 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?

Answer 1

On Saturday, when 12 weeks passed

Explanation:

Tom gets his hair cut every 3 weeks.

David gets his hair cut every 4 weeks.

Find the least common multiple of numbers 3 and 4:

`3=3\\ \\4=2\cdot 2\\ \\LCM(3,4)=3\cdot 2\cdot 2=12`

This means that Tom and David will get their hair cut on the same day at 12th week (if the first week when they started has number 0).

You can think in another way:

Tom gets his hair cut every 3 weeks. He got his hair cut after 3 weeks, after 6 weeks, after 9 weeks, after 12 weeks passed.

David gets his hair cut every 4 weeks. He got his hair cut after 4 weeks, after 8 weeks, after 12 weeks passed.