Example 1­Finding the Least Common Multiple
Find the least common multiple of 6 and 9.
6.4 Least Common Multiple
Solution
With small numbers, you can list multiples of each number.
Number:
Goal 1: Finding the Least Common Multiple
6
9
Multiples:
Least Common Multiple:
A number that is a multiple of two natural numbers is a common multiple of them. Of all the common multiples of two numbers, the smallest is the least common multiple (LCM).
Example 2­Finding the Least Common Multiple
Find the least common multiple of 180 and 378.
With large numbers, you can find the least common multiple by writing
the prime factorization of each number.
Number:
180
378
Prime Factors:
Common Factors:
Not Common Factors:
Least Common Multiple:
*The least common multiple is the product of the common prime factors and all the prime factors that are not common.*
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Goal 2: Using a Least Common Multiple
Example 4­Finding the LCM of Variable Expressions
Example 3­Using a Least Common Multiple
Find the least common multiple (LCM) of 10ab and 6b.
You have a box of tiles, each of which is 4 in. by 6 in. Without overlapping or cutting the tiles, what is the least number of tiles you need to form a square region?
Solution
Expression
10ab
Prime Factors
Common
Not Common
6b
Solution
Find the least common multiple (LCM).
*Remember, the least common multiple is the product of the common
prime factors and all the prime factors that are not in common.*
LCM=
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On Your Own:
1. List the first 4 multiples of 6.
2. Find the LCM of 3 and 9.
3. Find the LCM of 5, 10, and 20.
4. Find the LCM of 90 and 108.
5. Find the LCM of 2x3y and 3xy5.
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