The factors of 12 and 18 both include 1, 2, 3, and 6. The greatest of those is 6.
Greatest common factor is the largest number that divides both numbers exactly.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
The multiples of 4 and 6 first meet at 12.
Least common multiple is the smallest number that both numbers divide into.
Telling them apart
A common factor is at most the smaller number. A common multiple is at least the larger.
Factoring out
12 + 18 can be written 6(2 + 3), because 6 divides both.
What each one is
The greatest common factor of two numbers is the largest number dividing both. The least common multiple is the smallest number both divide into. GCF is about what they share going down; LCM about where they first meet going up.
Finding them by listing
For 12 and 18: factors of 12 are 1, 2, 3, 4, 6, 12; of 18 are 1, 2, 3, 6, 9, 18. The greatest shared one is 6. Multiples of 12 are 12, 24, 36; of 18 are 18, 36. The least shared one is 36. Listing works and is worth doing before learning shortcuts.
Using prime factors
12 = 2 × 2 × 3 and 18 = 2 × 3 × 3. The GCF takes the primes both share: 2 × 3 = 6. The LCM takes everything, using the highest count of each: 2 × 2 × 3 × 3 = 36. This method scales to numbers far too large to list.
What they are for
The GCF simplifies fractions and factors expressions. The LCM finds common denominators and answers questions about events that repeat on different cycles — two buses leaving every 12 and 18 minutes next coincide after 36.
Step 2: Try It Yourself
Tap and try it out.
The ringed squares are the multiples of 4. They land in a pattern.
Step 3: Watch an Example
One step at a time.
Watch Ana Factor Out
Ana rewrites 20 + 30 using a common factor.
- Step 1
She lists what divides both: 1, 2, 5, and 10.
Step 4: Your Turn
Practice makes it stick.
The Bags
Problem 1 of 2
24 apples and 36 pears into identical bags. What is the greatest number of bags?
bags
The Buses
Problem 2 of 2
One bus every 6 minutes, another every 8. After how many minutes do both come together?
minutes
Shared Factors and Multiples
1 of 4
Greatest common factor of 18 and 24?
2 of 4
Least common multiple of 4 and 10?
3 of 4
Greatest common factor of 15 and 25?
4 of 4
14 + 21 = 7(2 + ?). What is the missing number?
Step 5: Quick Check
Show what you know.
Question 1 of 2
Greatest common factor of 16 and 40?
Question 2 of 2
Which is never bigger than the smaller number?
What You Learned
- A common factor divides both numbers.
- A common multiple is divided by both.
- The greatest common factor can be taken outside a sum.