Greatest Common Factor and Least Common Multiple Test – Grade 6 Math (Printable PDF)

Question 1 Factors and multiples (2 points)

1. List all the factors of 36. (1 point)
2. List the first five multiples of 7. (1 point)

Question 2 Prime factorization (2 points)

Write the prime factorization of each number. Use exponents where helpful.

1. 150 (1 point)
2. 168 (1 point)

Question 3 Finding GCFs (2 points)

Find the greatest common factor.

1. 54 and 90 (1 point)
2. 63 and 98 (1 point)

Question 4 Finding LCMs (2 points)

Find the least common multiple.

1. 11 and 4 (1 point)
2. 6 and 10 (1 point)

Question 5 Factoring a sum (2 points)

The bars show two quantities, 32 and 56. Use their GCF to write 32 + 56 as a product.

1. Find the GCF of 32 and 56. (1 point)
2. Write 32 + 56 as GCF × (sum). (1 point)

Question 6 Factor tree for 132 (2 points)

A student started this factor tree. Complete it, then write 132 as a product of primes.

Question 7 Packing fruit baskets (2 points)

A stand has 64 oranges and 96 apples. All the fruit goes into identical baskets with nothing left over.

1. What is the greatest number of baskets? (1 point)
2. How many oranges and apples are in each basket? (1 point)

Question 8 Runners on a track (3 points)

Two runners start together at the same spot on a loop. Jin completes a lap every 8 minutes and Carla every 10 minutes.

1. After how many minutes are they next together at the start? Show the work. (1 point)
2. How many laps has each runner finished by then? (2 points)

Question 9 Two mystery numbers (3 points)

Two whole numbers have a GCF of 9 and an LCM of 54. One of them is 18. Find the other number and show that it works.