Question

# Use least commin multiple or greatest common divisor to solve the prob

Factors and multiples
Use least commin multiple or greatest common divisor to solve the problem.
Rob can complete his bus route in 6 hours. Joan can complete her bus route in 4 hours. If they both left the terminal at 3:00 am and after each completed route returned to the terminal, determine the next time they would leave the terminal at the same time.
A) 9:00 am
B) 7:00 am
C) 3:00 pm
D) Not enough information given to tell.

2021-08-10
Step 1
Given- Rob can complete his bus route in 6 hours. Joan can complete her route in 4 hours. If they both leave the terminal at 3:00 am and after each completed route return to the terminal,
To find- The next time they would leave the terminal at the same time.
Concept Used- To find the time at which they leave terminal , the concept of least common multiple can be used here.
Step 2
Explanation- As per the question, Rob can complete his bus route in 6 hours. Joan can complete her route in 4 hours.
Here using the least common multiple, so we have to find the multiples of 4 and 6 which are given below,
Multiple of $$\displaystyle{4}={4},{8},{12},{16},{20}\ldots\ldots$$
Multiple of $$\displaystyle{6}={6},{12},{18},{24},{30}\ldots\ldots.$$
From the above multiples, we see that 12 is the common multiple of 4 and 6.
So, the least common multiple of 4 and 6 is 12.
So, they will meet at the terminal after $$\displaystyle{\left({3}:{00}{a}{m}+{12}{h}{o}{u}{r}{s}\right)}={3}:{00}$$ pm.
Answer: Hence, the next time they would leave the terminal at 3:00 pm, which is option C.