3.2 Least Common Multiple
Learning Objectives:
1. Find the Least Common Multiple (LCM) using multiples of the largest number.
2. Find the Least Common Multiple (LCM) using Prime Factorization.
3. Write equivalent fractions when given a denominator.
4. Key Vocabulary: least common multiple (LCM).
A. Finding the Least Common Multiple (LCM) using multiples of the largest number
Method 1: Finding the LCM of a List of Numbers Using Multiples of the Largest Number.
1. Write the multiples of the largest number (Starting with the number itself) until a multiple
common to all numbers in the list is found.
2. The multiple found in Step 1 is the LCM.
Example 1. Find the Least Common Multiple using multiples of the largest number: 10, 15, 35
B. Finding the Least Common Multiple (LCM) using Prime Factorization
Method 2: Finding the LCM of a List of Numbers Using Prime Factorization.
1. Write the prime factorization of each number using exponent.
2. For each different prime factor in Step 1, circle the greatest number or time that factor occurs
or the highest exponent in any one factorization.
3. The LCM is the product of the circles factors.
Example 2. Find the Least Common Multiple using Prime Factorization:
C.
7, 14, 21, 36
Writing equivalent fractions when given a denominator
Example 3. Write each fraction as an equivalent fraction with the given denominator.
12
=
7 105