How To Solve LCM Problems

The steps for solving GCF and LCM problems tend to get jumbled up in the minds of students. They have a vague sense of dividing or multiplying, but often are not confident about what to do and only loosely remember the steps they should follow.

Using more concrete problem-solving strategies will help students solve these problems more effectively, and also give them confidence about what they are doing. 

A classic LCM problem has two different events, each occurring every so many days. 

Frisco the dog gets walked every 4 days, and goes to the dog park every 6 days. Frisco walked and went to the park today. How many days until the next time both events occur on the same day again.

At this point, many students might say the answer is 24. Others will confuse this with a GCF problem and say the answer is 2. Creating a visual model of the problem will help students see what they are supposed to find rather than just try to remember the ladder model or prime factorization.

Methods to Solve LCM Problems

Making a Model

Make a number line showing the days Frisco will get walked. Each jump on the number line represents a span of 4 days.

Make a second number line showing the days Frisco will go to the dog park. Each jump on the number line represents a span of 6 days.

Look for numbers that appear on both number lines. In this case 12 and 24. We are looking for “the next time” so the answer is 12. Frisco will get walked in 12 days. Frisco will go to the dog park in 12 days. Twelve days is the first time that both events will occur on the same day again. 

Listing Multiples

The problem can also be solved by listing multiples. The multiples of 12 and 24 appear on both lists, but 12 is the multiple that will occur first. This strategy only makes sense if a student understands why multiples matter. 

Also read: How To Solve Reciprocals in Equations

Frequently Asked Questions on LCM Problems