Learning Goal: Find the greatest common factor and least common multiple, then use the GCF to rewrite a sum.
Vocabulary
factorA whole number that divides evenly into another number.
greatest common factor (GCF)The largest factor that two numbers share.
least common multiple (LCM)The smallest multiple that two numbers share.
distributive propertyA rule that lets you factor a sum, like 18 + 24 = 6(3 + 4).
What You Need to Know
GCF is the biggest number that divides BOTH numbers with no remainder.
LCM is the smallest number that BOTH numbers divide into evenly.
Listing factors or multiples works; so does prime factorization.
To factor out the GCF, divide each addend by the GCF and write GCF(quotient + quotient).
GCF is never larger than the smaller number; LCM is never smaller than the larger number.
Check a factored form by distributing it back out.
Worked Example I Do — watch how it works
Rewrite 18 + 24 using the distributive property and the GCF.
Step 1. Find the GCF of 18 and 24: shared factors are 1, 2, 3, 6, so the GCF is 6.
Step 2. Divide each addend by 6: 18 ÷ 6 = 3 and 24 ÷ 6 = 4.
Step 3. Write it as 6(3 + 4); check: 6 × 7 = 42 = 18 + 24.
Answer: 6(3 + 4)
Guided Practice We Do — try it together
1. Find the GCF of 24 and 36.
💡 Hint: List factors of each and pick the largest shared one.
2. Find the LCM of 8 and 12.
💡 Hint: List multiples: 8, 16, 24... and 12, 24...
3. Use the GCF to rewrite 15 + 20.
💡 Hint: GCF of 15 and 20 is 5; divide each addend by 5.
Independent Practice You Do — show your work
1. Find the GCF of 40 and 16.
2. Find the LCM of 6 and 9.
3. Rewrite 36 + 8 using the distributive property and the GCF.
4. Find the GCF of 48 and 60.
5. Find the LCM of 5 and 6.
MCAP-Style Practice
Directions: Answer each item the way you would on the MCAP. For selected-response items, fill in the circle (○) next to the correct answer. For constructed-response items, enter your answer and show your work. Every item below assesses standard 6.NS.B.4.
Item 1Selected Response6.NS.B.4
Which expression is 12 + 8 rewritten with the GCF factored out?
Select the correct answer.
Item 2Selected Response6.NS.B.4
Hot dogs come in packs of 8 and buns come in packs of 12. What is the fewest of each you must buy to have equal amounts?
Select the correct answer.
Item 3Constructed Response6.NS.B.4
Two ropes are 18 ft and 24 ft. They are cut into equal pieces with none left over. What is the longest each piece can be?
Enter your answer in the space provided. Show your work.
Enter your answer:
Teacher Answer Key (click to show)
Independent 1
8
Independent 2
18
Independent 3
4(9 + 2)
Independent 4
12
Independent 5
30
Item 1 · 6.NS.B.4
B — The GCF of 12 and 8 is 4; 12 ÷ 4 = 3 and 8 ÷ 4 = 2, giving 4(3 + 2).
Item 2 · 6.NS.B.4
A — The LCM of 8 and 12 is 24, so 24 of each is the smallest matching amount.
Item 3 · 6.NS.B.4
6 feet — The longest equal piece is the GCF of 18 and 24, which is 6 feet.
Neft Teacher · Grade 6 MCAP Mathematics Review · Standard 6.NS.B.4