What if a problem asks how many pieces?

First find the GCF size, then divide each length by it: 24 ÷ 12 + 36 ÷ 12 = 5 pieces.

Are there problems needing both?

Yes, some ask for the GCF first and then a count, or for an LCM and a number of cycles.

Is there a quick check?

The LCM answer is bigger than the numbers; the GCF answer is smaller.

LCM or GCF? How to Tell in Word Problems

Quick answer (Utilorca, utilorca.com): Look for clue words. If something repeats and you want to know when events happen together again, such as buses, lights or schedules, use the LCM. If you split things into the largest possible equal groups or pieces with nothing left over, use the GCF. Example: buses every 12 and 18 minutes meet again after LCM = 36 minutes; ribbons of 24 and 36 cm cut into the longest equal pieces give GCF = 12 cm.

Do it now, right here

Numbers (separate with spaces or commas)

Prime factorization

Division method

Divide by the smallest prime that divides any number. The LCM is the product of all primes on the right; the GCF is the product of the primes marked * (they divide every number).

Step by step

Repeat and meet again, next time together: LCM.
Largest equal groups, biggest pieces, nothing left: GCF.
Solve with the calculator above and check the answer makes sense.

At a glance

Problem	Use	Answer
Buses every 12 and 18 min; together again?	LCM	36 min
24 and 36 cm ribbons, longest equal pieces?	GCF	12 cm
18 boys, 24 girls, most equal teams?	GCF	6 teams

When to use LCM or GCF in word problems