Free Printable LCM and GCF Worksheets for Grade 6

In 6th grade, students formalize their understanding of these concepts. A key new application is using the GCF to rewrite sums using the distributive property. For example, students learn to express 36 + 8 as 4(9 + 2). They are expected to find the GCF of two numbers up to 100 and the LCM of two numbers up to 12.

Model the process as "factoring out" the GCF. Start with an expression like 18 + 24. Guide students to find the GCF, which is 6. Then, show them how to rewrite the expression as (6 × 3) + (6 × 4), which can be expressed as 6(3 + 4). Using area models can also be an effective visual strategy for this concept.

The worksheets include procedural practice for finding GCF and LCM with larger numbers. They also feature problems requiring students to apply the distributive property to express a sum of two numbers as a multiple of a sum. Word problems that require students to choose between finding the GCF or LCM are also included to build reasoning skills.

At this stage, a primary challenge is applying the correct concept to word problems. Students often struggle when the problem doesn't explicitly state whether to find the GCF or LCM. They need practice analyzing a problem's context to determine which calculation is required, such as recognizing that "splitting into identical groups" implies GCF, while "events happening at the same time again" implies LCM.

These worksheets are ideal for reinforcing classroom lessons, for homework, or as a quick formative assessment. You can assign them digitally on Wayground or print the PDF versions for offline work. For paper assignments, the Wayground for Teachers app lets you scan and grade student work efficiently using the provided answer key.

This work is directly aligned with Common Core standard 6.NS.B.4. This standard explicitly requires students to find the greatest common factor and least common multiple of two whole numbers. It also requires them to use the distributive property to express a sum of two whole numbers with a common factor, making these worksheets a perfect resource for targeted practice.