Read the Situation
Identify the quantities, the goal, and the conditions described in the problem.
Free Interactive Math Tool
GCF and LCM Word Problems
Decide whether each situation requires the greatest common factor or least common multiple, solve the problem, and explain what the answer means in context.
Learn How to Choose the Correct Strategy
Learn how equal groups, no leftovers, repeating schedules, and first shared events help determine whether a word problem requires the GCF or LCM.
Read the GCF and LCM Word Problems GuideHow It Works
Solve the Situation, Not Just the Numbers
The important skill is recognizing what the question is asking before calculating anything.
Choose GCF or LCM
Decide whether the situation needs the greatest equal grouping or the first shared multiple.
Calculate the Value
Find the GCF or LCM of the quantities given in the problem.
Interpret the Answer
State what the calculated number represents in the original situation.
Interactive Practice
GCF or LCM?
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Problems
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Streak
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Equal Groups
MediumMaya has 24 red markers and 36 blue markers. She wants to make the greatest possible number of identical supply kits with no markers left over. How many kits can she make?
Quantity 1:
24
Quantity 2:
36
1
Choose a Strategy
2
Calculate
3
Interpret
Step 1
Does this situation require the GCF or LCM?
Think about the goal of the problem—not just individual keywords.
Step 2
Find the Greatest Common Factor
Find the GCF of the two important quantities.
GCF(24, 36)
kits
Step 3
What does the answer mean?
Choose the statement that correctly interprets the calculated value in the original situation.
Excellent!
You selected the correct strategy, calculated the result, and interpreted the answer correctly.
Strategy
GCF
Calculation
GCF(24, 36) = 12
Meaning
Maya can make 12 identical kits.
The GCF is used because the quantities are being divided into the greatest possible number of equal groups with no leftovers.
Choosing the Operation
Understand the Structure of the Problem
Keywords can help, but the mathematical goal of the situation is more reliable.
Use GCF for Equal Groups
Use the GCF when quantities are divided into the greatest possible number of identical groups with nothing left over.
Use LCM for Repeating Events
Use the LCM to find the first time repeating events happen together or the smallest shared amount that fits multiple group sizes.
Ask What the Answer Represents
Before calculating, predict whether the answer will represent groups, items per group, time, distance, or another quantity.
Do Not Trust One Keyword
Words such as “greatest,” “least,” or “each” are not enough by themselves. Read the entire relationship described in the problem.
Common Situations
Where GCF and LCM Word Problems Appear
Kits, Bags, and Teams
Divide several quantities into the greatest number of identical groups without leftovers.
Repeating Schedules
Determine when buses, lights, alarms, or other repeating events will occur together again.
Equal-Length Pieces
Cut different lengths into the longest equal pieces with no material left over.
Matching Package Sizes
Find the smallest shared quantity that can be made from items sold or arranged in different group sizes.
Practice Another Word Problem
Every new problem gives you another opportunity to choose the correct strategy, solve accurately, and explain the meaning of your answer.