📚 Practice With Worksheets
Practice identifying common factors, calculating GCF and LCM, and applying both concepts to word problems.
▶️ Learn With Videos
Review several methods for finding the greatest common factor and least common multiple.
🛠️ How to Use This Tool
Choose Greatest Common Factor, Least Common Multiple, or Mixed GCF and LCM Practice. Then select numbers only or a combination of computation and word problems.
For mixed word problems, first decide whether the situation requires GCF or LCM. Then enter the requested number, arrangement, group size, or common occurrence.
Select Check Answer for feedback. After making a valid attempt, use Show Solution to review factors, multiples, and the reasoning used to interpret the situation.
🧠 Things to Notice
GCF situations usually divide existing quantities into the greatest number of identical groups or the largest equal pieces with nothing left over.
LCM situations usually involve repeating events, matching package quantities, or finding the first amount or time shared by two patterns.
Keywords can provide clues, but the structure of the situation matters most. Ask whether the quantities are being divided into smaller equal groups or increased until they meet.
📘 Vocabulary
Factor: A whole number that divides another whole number evenly.
Factor pair: Two whole numbers whose product equals a given number.
Common factor: A factor shared by two or more whole numbers.
Greatest common factor: The greatest whole number that divides every given number evenly.
GCF: An abbreviation for greatest common factor.
Multiple: The product of a given number and a whole number.
Common multiple: A multiple shared by two or more whole numbers.
Least common multiple: The least positive multiple shared by every given number.
LCM: An abbreviation for least common multiple.
Divisible: Able to be divided by a whole number without a remainder.
Identical groups: Groups containing the same number and type of each item.
No remainder: A condition in which every item is used and nothing is left over.
Repeating event: An event that occurs again after a regular interval.
Interval: The amount of time or distance between repeated events.
Common occurrence: A time or position at which two or more repeating patterns happen together.
📐 GCF and LCM: Compare and Contrast
Both concepts involve relationships shared by two or more whole numbers, but they answer different kinds of questions.
Greatest Common Factor
Main idea: Find the greatest factor that divides every given number evenly.
Think: Divide the original quantities into smaller equal groups or pieces.
Common situations: identical groups, equal packages, rows, teams, bouquets, longest equal pieces, and largest square tiles.
Common clues:
Least Common Multiple
Main idea: Find the least positive multiple shared by every given number.
Think: Increase the original numbers by listing multiples until the patterns meet.
Common situations: repeating schedules, flashing lights, common arrivals, matching package quantities, and first shared events.
Common clues:
What GCF and LCM Have in Common
Both use factors, multiples, multiplication, and division.
Both identify values that work for every given number.
The wording and structure determine which concept is appropriate.
Decision question: Are you dividing existing quantities into the greatest equal groups or pieces? Think GCF. Are you increasing repeating quantities until they meet at the first shared value? Think LCM.
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