Math Snap

STEP 1

Assumptions1. The first person takes21 minutes to complete one round.
. The second person takes45 minutes to complete one round.
3. Both start running from the same place at the same time.
4. They continue to run until they meet again at the starting point.

STEP 2

We need to find the least common multiple (LCM) of the two times. The LCM of two numbers is the smallest number that is a multiple of both numbers. This will give us the time it takes for both people to meet at the starting point again.
$$LCM = LCM(21,45)$$

STEP 3

First, we need to find the prime factorization of both numbers.For21, the prime factorization is $3 \times7$.
For45, the prime factorization is $3^2 \times5$.

STEP 4

To find the LCM, we take the highest power of each prime number from the factorizations of both numbers.
So, the LCM is $3^2 \times \times7$.

Calculate the LCM.
$$LCM =3^2 \times5 \times7 =9 \times5 \times7 =315$$So, it will take315 minutes for the two people to meet again at the starting point.