Least Common Multiple
Warm-Up!
Coach instructions: Give
students 5 to 10 minutes
to go through the warm-up
problems.
Try these problems before watching the lesson.
1. What is the smallest two-digit number that is a multiple of 2 and 3?
The product of 2 and 3 is 6. If we double it, we get the smallest two-digit multiple or 12.
2. What is the smallest number that is a multiple of 2, 3 and 5?
If we multiply the 2 · 3 · 5 we get 30.
3. What is the smallest perfect square that is divisible by both 2 and 3?
If we go through our perfect squares until we get a multiple of 2 and 3, we look at 1, 4, 9, 16,
25 and stop at 36.
4. How many positive integers less than 100 are multiples of 2, 3 and 5?
In problem 2, we saw the smallest multiple of these three numbers was 30. This means that
60 and 90 are also multiples. Giving us 3 positive integers.
Take a look at the following problems and follow along as they are explained in the video.
5. What is the least common multiple of 84 and 63?
Solution in video. Answer: 252.
6. Mrs. Chandler has a class of 20 kids and she wants to give each student at least one pencil to use
at MATHCOUNTS practices. Pencils are sold in packages of 12. If Mrs. Chandler wants to give
each student the same number of pencils with no extra leftover, what is the smallest number of
packages of pencils she could buy?
Solution in video. Answer: 5 packages.
7. George Washington High School’s marching band members can evenly arrange themselves in
rows of 8,9, 10 or 12. What is the least number of students that could be in the marching band?
Solution in video. Answer: 360 students.
Coach instructions: After
students try the warm-up
problems, play the video and
have them follow along with
the solutions.
The Problems
