6th Grade Greatest Common Factor and Least Common Multiple Test with Point Values (PDF)

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

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

This 45-minute test has 9 questions worth 20 points. It covers factors, GCF, LCM, prime factorization, the distributive property, and word problems (Common Core 6.NS.B.4). Show your work for full credit.

Time and points

About this test

Grade: Grade 6
Chapter: Greatest Common Factor and Least Common Multiple
Standards: 6.NS.B.4
Time: 45 minutes
Total: 20 points

Gcf lcm test: questions

Question 1 – Factors [2 pts]

List all the factors of 40.

Question 2 – GCF [2 pts]

Find the greatest common factor of 36 and 54.

Question 3 – LCM [2 pts]

Multiples of 6 and 9.

Find the least common multiple of 6 and 9.

Question 4 – Prime factorization [2 pts]

A factor tree for 72.

Write the prime factorization of 72 using exponents.

Question 5 – Distributive property [2 pts]

Write \(54 + 81\) as a product of the GCF and a sum.

Question 6 – Schedules [2 pts]

Flashes every 12 seconds and every 18 seconds.

A lighthouse flashes every 12 seconds. A buoy light flashes every 18 seconds. They flash together at 0 seconds. When do they flash together next?

Question 7 – Sharing equally [2 pts]

Noah has 48 red beads and 60 blue beads. He makes identical bracelets using all the beads. Find the greatest number of bracelets.

Question 8 – Fruit trays [3 pts]

A school fair has 56 apples and 42 oranges. Volunteers make identical fruit trays using all the fruit. Find the greatest number of trays, the number of each fruit per tray, and write 56 + 42 using the GCF.

Question 9 – Two schedules [3 pts]

Sofia practices piano every 3 days, soccer every 4 days, and art every 6 days. She does all three today. Find how many days until she does all three on the same day again.

Key facts behind this gcf lcm test

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

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All Grade 6 chapters: Grade 6 math.

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