LEAST COMMON MULTIPLE (LCM)
Use one of these two methods to find the LCM of two or more numbers.
Method I: Individual Prime Factoring Method
1. Find the prime factorization of each
number in the group.
2. Make a list of ALL factors, raised to
the HIGHEST power that appears in
any factorization.
3. Multiply out.
Example: Find the LCM of 40 and 60.
Make a list of ALL of the prime factors:
2, 3 & 5.
Raise each factor to the highest power that
appears on either list and multiply the complete
list of factors:
LCM = 23 3 5 = 120.
Method II: Group-Factoring Method
1. Using prime numbers as divisors,
divide each number in the group, if
possible. When a number is not
divisible by the prime divisor just
bring it down to the next row along
with the quotients from the other
divisions. Continue dividing by
prime divisors until all quotients are
ones.
2. Multiply all of the prime divisors –
the product is the LCM.
Example: Find the LCM of 40 and 60.
60
6
10
2
3
2
5
2 2 3 5 = 22 3
5
40
4
10
2
2
2
5
2 2 2 5 = 23 5
2 ) 60 40
2 ) 30 20
2 ) 15 10
3 ) 15 5
5 ) 5 5
1 1
LCM = 23 3 5 = 120
Remember: A Least Common Denominator (LCD) is nothing more than
the LCM of the denominators of a group of fractions. Use the same steps
listed above to find an LCD. LCDs are required for addition and
subtraction of fractions and not required for multiplication and division.
