← Back to the Greatest Common Factor And Least Common Multiple worksheet
Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Standards: 6.NS.B.4 · Level: Grade 6
Problem 1 Listing factors
Pairs that multiply to 28: 1 × 28, 2 × 14, 4 × 7. Factors: 1, 2, 4, 7, 14, 28.
Problem 2 Smallest multiples
13 × 1 through 13 × 6: 13, 26, 39, 52, 65, 78.
Problem 3 Prime or composite
51 = 3 × 17, composite. 53 is not divisible by 2, 3, 5 or 7, so it is prime. 57 = 3 × 19, composite. 61 is not divisible by 2, 3, 5 or 7, prime. Prime: 53, 61. Composite: 51, 57.
Problem 4 Finishing a factor tree
9 = 3 × 3 and 10 = 2 × 5.
90 = 2 × 3 × 3 × 5, or 2 × 32 × 5.
Problem 5 GCF of 20 and 50
Factors of 20: 1, 2, 4, 5, 10, 20. Factors of 50: 1, 2, 5, 10, 25, 50. Common: 1, 2, 5, 10. GCF = 10.
Problem 6 GCF of 42 and 56
42 = 2 × 3 × 7 and 56 = 2 × 2 × 2 × 7. Shared primes: 2 and 7. 2 × 7 = 14. Check: 42 ÷ 14 = 3 and 56 ÷ 14 = 4.
Problem 7 LCM of 5 and 12
Multiples of 12: 12, 24, 36, 48, 60. Only 60 is also a multiple of 5 (60 = 5 × 12). LCM = 60.
Problem 8 Multiples of 10 and 4
Multiples of 10: 10, 20, 30, 40. The first one that is also a multiple of 4 is 20 (20 = 4 × 5).
LCM = 20.
Problem 9 GCF of 64 and 80
64 = 26 and 80 = 24 × 5. Shared: 24 = 16. Check: 64 ÷ 16 = 4, 80 ÷ 16 = 5, and 4 and 5 share no factor. GCF = 16.
Problem 10 LCM of 9 and 12
Multiples of 12: 12, 24, 36. 36 ÷ 9 = 4, so 36 is a multiple of 9, while 12 and 24 are not. LCM = 36.
Problem 11 GCF of 45 and 100
45 = 3 × 3 × 5 and 100 = 2 × 2 × 5 × 5. The only shared prime is 5. GCF = 5.
Problem 12 Factoring 24 + 36
GCF(24, 36) = 12. 24 = 12 × 2 and 36 = 12 × 3.
24 + 36 = 12(2 + 3). Check: 12 × 5 = 60.
Problem 13 Factoring 63 + 84
GCF(63, 84) = 21, since 63 = 21 × 3 and 84 = 21 × 4. 63 + 84 = 21(3 + 4). Check: 21 × 7 = 147 = 63 + 84.
Problem 14 GCF of 84 and 126
84 = 2 × 2 × 3 × 7 and 126 = 2 × 3 × 3 × 7. Shared primes: 2, 3 and 7. 2 × 3 × 7 = 42.
Problem 15 Gift bags
GCF(56, 84) = 28. 56 ÷ 28 = 2 and 84 ÷ 28 = 3. 28 bags, each with 2 granola bars and 3 juice boxes.
Problem 16 Lighthouse flashes
LCM(6, 8) = 24, so they flash together every 24 seconds. 2 minutes = 120 seconds. Times: 24, 48, 72, 96, 120. 5 times.
Problem 17 Square garden plots
GCF(96, 60) = 12, so the squares are 12 ft wide. Columns: 96 ÷ 12 = 8. Rows: 60 ÷ 12 = 5.
8 × 5 = 40. 12 ft squares, 40 plots.
Problem 18 Two bus routes
LCM(10, 15) = 30. Adding 30 minutes repeatedly: 7:30 AM, 8:00 AM, 8:30 AM and 9:00 AM.
Problem 19 School supply packs
LCM(8, 12) = 24 items. Marker packs: 24 ÷ 8 = 3. Note packs: 24 ÷ 12 = 2. 24 of each, using 3 marker packs and 2 sticky-note packs.
Problem 20 Missing number
For two numbers, GCF × LCM = product. 12 × 72 = 864, and 864 ÷ 24 = 36. Check: GCF(24, 36) = 12 and LCM(24, 36) = 72. The other number is 36.