Pre-Algebra · Quick Reference

Least Common Multiple Cheat Sheet

Pre-Algebra · Lesson 10/10

In one line: the least common multiple (LCM) is the smallest number that two or more numbers all divide into evenly — essential for adding fractions with different denominators.

Key Ideas

1Definition. The LCM of two or more numbers is the smallest positive number that is a multiple of all of them.

2Finding LCM by Listing Multiples. List the multiples of each number and find the smallest one they share.

3Finding LCM by Prime Factorization. Break each number into prime factors, then multiply together the highest power of every prime that appears in any of the numbers.

4LCM and Fractions. The LCM of the denominators gives the smallest common denominator needed to add or subtract fractions.

5LCM vs. GCF. GCF finds the largest shared factor (divides into the numbers); LCM finds the smallest shared multiple (the numbers divide into it).

Worked Examples

Find the LCM of 4 and 6.

LCM(4,6) = 12

Find the LCM of 9 and 12 using the GCF shortcut. (GCF(9,12)=3)

LCM(9,12) = 36

Add 1/6 + 1/4 by first finding the LCM of the denominators.

5/12

Formulas

LCM(a,b) = (a*b) / GCF(a,b)

Practice Yourself

Find the LCM of 3 and 5.

Find the LCM of 6 and 8.

Find the LCM of 10 and 15.