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Greatest Common Factor and Least Common Multiple Test Answer Key with Scoring – Grade 6

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Last updated: October 22, 2026 · Written by the Math Made Easy math teachers

Grade 6 Math Test Answer Keys – Mathbot, the Math Made Easy robot coach, with free printable test answer keys for Grade 6
Looking for a greatest common factor and least common multiple test answer key? Then this answer key gives the solutions and the scoring guide of the Grade 6 test on Factors, Multiples and Common Ones: GCF and LCM. Use this answer key to score the test. Each solution shows full work, and the scoring notes say how the points are awarded. Give partial credit when the reasoning is sound but a small slip appears.

Standards: 6.NS.B.4 · Level: Grade 6

Question 1 Factors and multiples (2 points)

(a) 1 × 36, 2 × 18, 3 × 12, 4 × 9, 6 × 6: 1, 2, 3, 4, 6, 9, 12, 18, 36.

(b) 7, 14, 21, 28, 35.

Scoring: 1 point per part; deduct for a missing factor.

Question 2 Prime factorization (2 points)

(a) 150 = 2 × 75 = 2 × 3 × 25 = 2 × 3 × 52.

(b) 168 = 2 × 84 = 2 × 2 × 42 = 2 × 2 × 2 × 21 = 23 × 3 × 7.

Scoring: 1 point per part.

Question 3 Finding GCFs (2 points)

(a) 54 = 2 × 33, 90 = 2 × 32 × 5. Shared: 2 × 3 × 3 = 18.

(b) 63 = 32 × 7, 98 = 2 × 72. Shared: 7.

Scoring: 1 point per part.

Question 4 Finding LCMs (2 points)

(a) 11 and 4 share no factor, so LCM = 11 × 4 = 44.

(b) Multiples of 10: 10, 20, 30. 30 is a multiple of 6. 30.

Scoring: 1 point per part.

Question 5 Factoring a sum (2 points)

(a) 32 = 25 and 56 = 23 × 7. The GCF is 23 = 8.

(b) 32 ÷ 8 = 4 and 56 ÷ 8 = 7, so 32 + 56 = 8(4 + 7). Check: 8 × 11 = 88.

8 × 48 × 732 + 56 = 8(4 + 7)
Common factor 8.

Scoring: 1 point per part.

Question 6 Factor tree for 132 (2 points)

4 = 2 × 2, so the primes are 3, 2, 2 and 11.

32241211132
Finished: 132 = 2 × 2 × 3 × 11.

132 = 22 × 3 × 11.

Scoring: 1 point for finishing the tree, 1 point for the product.

Question 7 Packing fruit baskets (2 points)

(a) GCF(64, 96) = 32 (64 = 26, 96 = 25 × 3). 32 baskets.

(b) 64 ÷ 32 = 2 and 96 ÷ 32 = 3: 2 oranges and 3 apples.

Scoring: 1 point per part.

Question 8 Runners on a track (3 points)

(a) LCM(8, 10): multiples of 10 are 10, 20, 30, 40; 40 = 8 × 5. 40 minutes.

(b) Jin: 40 ÷ 8 = 5 laps. Carla: 40 ÷ 10 = 4 laps.

Scoring: 1 point for (a); 1 point for each lap count in (b).

Question 9 Two mystery numbers (3 points)

GCF × LCM = product of the numbers: 9 × 54 = 486. 486 ÷ 18 = 27.

Check: 18 = 2 × 32 and 27 = 33, so GCF = 32 = 9 and LCM = 2 × 33 = 54. The other number is 27.

Scoring: 1 point for the product 486, 1 point for 27, 1 point for the check.

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