Page 383 - Algebra 1

L E S S O N Finding the Least Common Multiple 57
Warm Up
1. Vocabulary A ( prime, composite) number has exactly two
(38)
Find the prime factorization of each number. 2. 18 3. 110
(38) (38)
Factor using the greatest common factor.
4. (3x + 27) 5. (4x3 + 14x)
(38) (38)
factors, itself and one.
New Concepts The least number that is evenly divisible by each of the numbers in a set of numbers is called the least common multiple or LCM.
Finding the Least Common Multiple
1. Write each number as a product of prime factors.
2. Use every factor of the given numbers as a factor of the LCM. Use each factor the greatest number of times it is a factor of any of the numbers or expressions.
Example
1
Math Reasoning
Verify Show that 72 is the LCM of 24 and 36.
Online Connection www.SaxonMathResources.com
Identifying the LCM of a Set of Numbers
a. Find the LCM of 24 and 36.
SOLUTION
Write each number as a product of prime numbers. 24 = 2 · 2 · 2 · 3
36 = 2 · 2 · 3 · 3
The number 2 is a factor of both 24 and 36. The greater number of times it appears is three times in 24, so it will appear three times in the LCM.
2·2·2
The number 3 is a factor of both numbers as well. The greater number of times it appears is two times in 36, so it will also appear in the LCM two times.
LCM = 2 · 2 · 2 · 3 · 3 LCM = 72
The LCM of 24 and 36 is 72.
368 Saxon Algebra 1