6th Grade Greatest Common Factor and Least Common Multiple Test Solutions and Scoring (PDF)

6th Grade math test solutions: Greatest Common Factor and Least Common Multiple – Maths PDF

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This gcf lcm test answers for 6th Grade covers greatest common factor and least common multiple (Common Core 6.NS.B.4), with a free PDF to print.

Use this key to score the GCF and LCM test out of 20 points. Each solution is fully worked, and the scoring line explains how to award each point and partial credit.

Grade 6 · Common Core State Standards: 6.NS.B.4

Gcf lcm test answers: worked solutions

Question 1 – Factors [2 pts]

1, 2, 4, 5, 8, 10, 20, 40.

Scoring: 2 points for all eight; 1 point if one factor is missing or extra.

Question 2 – GCF [2 pts]

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36.

Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54.

Common factors: 1, 2, 3, 6, 9, 18. The greatest is 18.

Scoring: 1 point for the lists or prime factors; 1 point for 18.

Question 3 – LCM [2 pts]

Multiples of 6: 6, 12, 18, 24.

Multiples of 9: 9, 18, 27.

The first multiple on both lists is 18.

The first common multiple is 18.

Scoring: 1 point for listing multiples; 1 point for 18.

Question 4 – Prime factorization [2 pts]

\(72 = 2 \times 2 \times 2 \times 3 \times 3 = 2^{3} \times 3^{2}\).

Prime factors: 2, 2, 2, 3, 3.

Scoring: 1 point for the prime factors; 1 point for exponent form.

Question 5 – Distributive property [2 pts]

GCF of 54 and 81 is 27.

\(54 + 81 = 27(2 + 3)\).

Scoring: 1 point for the GCF; 1 point for the expression.

Question 6 – Schedules [2 pts]

LCM of 12 and 18 is 36.

They flash together after 36 seconds.

Scoring: 1 point for the method; 1 point for 36 seconds.

Question 7 – Sharing equally [2 pts]

GCF of 48 and 60 is 12.

He can make 12 bracelets.

Scoring: 1 point for the GCF method; 1 point for 12.

Question 8 – Fruit trays [3 pts]

GCF of 56 and 42 is 14, so 14 trays.

Each tray has \(56 \div 14 = 4\) apples and \(42 \div 14 = 3\) oranges.

\(56 + 42 = 14(4 + 3)\).

Scoring: 1 point for 14 trays; 1 point for the fruit per tray; 1 point for the expression.

Question 9 – Two schedules [3 pts]

LCM of 3, 4, and 6: multiples of 6 are 6, 12; 12 is a multiple of 3 and 4.

The LCM is 12.

She does all three again in 12 days.

Scoring: 1 point for the multiples or prime factors; 1 point for the LCM; 1 point for the conclusion.

Total score

Total

20 points

Key facts behind this gcf lcm test answers

Key facts

A factor divides a number evenly; a multiple is a product with a whole number.
The GCF is the largest shared factor.
The LCM is the smallest shared multiple.
Prime factorization helps: use the smaller exponents for the GCF and the greater for the LCM.
The GCF lets you write a sum as GCF times a sum, such as 36 + 48 = 12(3 + 4).

How to use this gcf lcm test answers

Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.

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