Florida Grade 6 Math · Number Sense and Operations

MA.6.NSO.3.1: Greatest Common Factor and Least Common Multiple

What this Grade 6 benchmark means, worked examples, common mistakes, and a free printable worksheet.

Created by a Florida mom · Published by Tropical Learning LLC

What Is Benchmark MA.6.NSO.3.1?

The greatest common factor (GCF) of two numbers is the largest number that divides both. The least common multiple (LCM) is the smallest number that is a multiple of both.

GCF problems usually split things into equal groups ("the most identical kits"). LCM problems usually ask when things happen together again. The GCF also simplifies fractions. In Grade 6, GCFs are within 1,000 and LCMs use factors up to 25.

Official benchmarkGiven a mathematical or real-world context, find the greatest common factor and least common multiple of two whole numbers.

On the FAST test: part of the Grade 6 reporting category Number Sense and Operations, which is about 33–42% of the test.

Worked Examples

Worked Example 1

Greatest Common Factor

A teacher has 24 pencils and 36 erasers. She wants to make identical kits using all of them. What is the greatest number of kits she can make?
  1. 1Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
  2. 2Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
  3. 3The greatest common factor is 12. Each kit has 24 ÷ 12 = 2 pencils and 36 ÷ 12 = 3 erasers.
Answer: 12 kits

Worked Example 2

Least Common Multiple

Adam works out every 8 days and Susan every 12 days. They both work out today. In how many days will they work out on the same day again?
  1. 1Multiples of 8: 8, 16, 24, 32, ...
  2. 2Multiples of 12: 12, 24, 36, ...
  3. 3The least common multiple is 24.
Answer: 24 days

Common Mistakes to Watch For

Mixing up GCF and LCM

Wrong:The GCF of 8 and 12 is 24.

24 is the LCM. The GCF is the largest number that divides both: 4.

Always multiplying the numbers to get the LCM

Wrong:The LCM of 6 and 8 is 48.

48 is a common multiple, but not the least. The LCM of 6 and 8 is 24.

Helpful Math Tip

Ask: "Are we splitting into equal groups (GCF) or waiting for things to line up again (LCM)?"

Related Grade 6 Skills

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Independent Educational Platform. FastChomp is published by Tropical Learning LLC and is not affiliated with, sponsored by, or endorsed by the Florida Department of Education. FAST and Star assessment names are referenced for informational purposes only. FastChomp practice questions are original educational materials, not official Florida FAST assessment questions.