ACT Math Word Problem?

Test Preparation ACT Preparation
1

Stan has to do physical therapy exercises twice a day. One set of exercises is to be done every 8 hours and the other is to be done every 6 hours. If Stan does both sets of exercises at 8:30 AM and does both sets on schedule, how many hours later will it be when he next does both sets of exercises at the same time?

F. 48
G. 24
H. 20
J. 13
K. 8

I know the answer is 24 but my teacher went through a complicated process of writing down all the times till they get to the same time. Couldn’t I just find the least common multiple of 6 and 8 to get 24 or will that not work for other questions?

2

it is 24 because that is a number both 8 and 6 go into.
6x4= 24 and 8x3 is 24

there is no number prior to 24 that both 6 and 8 divide into perfectly.

3

@DoctorMD Thanks that’s what I thought, I was just asking because my teacher said that writing down all the times was the only way to answer the question (btw I’m taking a Princeton Ultimate Course class for anyone wondering).