2. Least Common Multiple (LCM)
The Least Common Multiple (LCM) is also referred to as
the Lowest Common Multiple (LCM) and Least Common
Divisor (LCD). For two integers a and b, denoted LCM (a,
b), the LCM is the smallest positive integer that is evenly
divisible by both a and b. For example, LCM (2, 3) = 6 and
LCM (6, 10) = 30.
3. Least Common Multiple (LCM)
The LCM of two or more numbers is the smallest number
that is evenly divisible by all numbers in the set.
4. How to Find the Least Common Multiple
This LCM calculator with steps finds the LCM and shows
the work using 6 different methods:
a. Listing Multiples
b. Prime Factorization
c. Cake / Ladder Method
d. Division Method
e. Using the Greatest Common Factor GCF
5. How to Find LCM by Listing Multiples
1. List the multiples of each number until at least one of
the multiples appears on all lists.
2. Find the smallest number that is on all of the lists.
3. This number is the LCM.
6. Example 1:
LCM (6, 7, 21)
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60
Multiples of 7: 7, 14, 21, 28, 35, 42, 56, 63
Multiples of 21: 21, 42, 63
Find the smallest number that is on all of the lists.
We have it in bold above.
So LCM(6, 7, 21) is 42.
7. How to Find LCM by Prime Factorization
1. Find all the prime factors of each given number.
2. List all the prime numbers found, as many times as
they occur most often for any one given number.
3. Multiply the list of prime factors together to find
the LCM.
4. The LCM (a, b) is calculated by finding the prime
factorization of both a and b. Use the same process for the
LCM of more than 2 numbers.
8. Example 1:
For LCM (12, 30), we find:
Prime factorization of 12 = 2 × 2 × 3.
Prime factorization of 30 = 2 × 3 × 5.
Using all prime numbers found as often as each
occurs most often we take 2 × 2 × 3 × 5 = 60.
Therefore LCM (12, 30) = 60.
9. Example 2:
For LCM (24, 300), we find:
Prime factorization of 24 = 2 × 2 × 2 × 3.
Prime factorization of 300 = 2 × 2 × 3 × 5 × 5.
Using all prime numbers found as often as each
occurs most often we take 2 × 2 × 2 × 3 × 5 × 5 = 600.
Therefore LCM (24, 300) = 600.
10. Activity 1:
List down the next 10 multiples of the following numbers. Use the first number as your
example.
1. 10 - _____, _____, _____, _____, _____
2. 15 - _____, _____, _____, _____, _____
3. 11 - _____, _____, _____, _____, _____
4. 25 - _____, _____, _____, _____, _____
5. 21 - _____, _____, _____, _____, _____
6. 13 - _____, _____, _____, _____, _____
7. 12 - _____, _____, _____, _____, _____
8. 9 - _____, _____, _____, _____, _____
9. 35 - _____, _____, _____, _____, _____
10. 6 - _____, _____, _____, _____, _____
11. Activity 1:
List down the next 10 multiples of the following numbers. Use the first number as your
example.
11. 24 - _____, _____, _____, _____, _____
12. 14 - _____, _____, _____, _____, _____
13. 50 - _____, _____, _____, _____, _____
14. 8 - _____, _____, _____, _____, _____
15. 22 - _____, _____, _____, _____, _____
16. 16 - _____, _____, _____, _____, _____
17. 30 - _____, _____, _____, _____, _____
18. 7 - _____, _____, _____, _____, _____
19. 5 - _____, _____, _____, _____, _____
20. 20 - _____, _____, _____, _____, _____
12. Activity 2:
Find and encircle the LCM of the following numbers using the listing method: Use the first number as
your example.
1. 4 and 22 2. 6 and
24
4 ______________________________ 6
______________________________
22 ______________________________ 24
______________________________
3. 8 and 6 4. 3 and
4
8 ______________________________ 3
______________________________
13. Activity 2:
5. 10 and 23 6. 2 and 4
10 ______________________________ 2
______________________________
23 ______________________________ 4
______________________________
7. 16 and 24 8. 28 and 6
16 ______________________________ 28
______________________________
24 ______________________________ 6
______________________________
9. 10 and 19 10. 14 and 28
