Factors · Capstone · C1

GCF or LCM?

The deciding skill: GCF for splitting into the largest equal groups or simplifying; LCM for when repeating things line up or for a common denominator. Read the problem, then choose — and compute.

01 / THE IDEA

See it work.

Watch the method

GCF or LCM?

Sharing into equal groups → GCF; lining up → LCM.

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gcd⁡ or LCM?\gcd \text{ or LCM?}
1

Which tool?

Sharing/grouping into equal parts → GCF. Events repeating/lining up → LCM.

— / WHY IT WORKS

The idea underneath.

The decision

Largest equal groups, or simplest fraction → GCF (a factor). Next time events coincide, or a common denominator → LCM (a multiple).

Why it works

Smaller answer? GCF. Bigger? LCM.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

You want to split 24 pens and 36 pencils into identical packs with none left over, using the largest pack size. Do you use the GCF or the LCM?

1

Answer

GCF

EX 2medium

You want to split 24 pens and 36 pencils into identical packs with none left over, using the largest pack size. Do you use the GCF or the LCM?

1

Answer

GCF

EX 3hard

Two buses leave together; one every 12 min, one every 18 min. To find when they next leave together, do you use the GCF or the LCM?

1

Answer

LCM

04 / COMMON TRAPS

Where students slip.

Trap

Swapping GCF and LCM.

Fix

GCF is a shared FACTOR (≤ the numbers); LCM is a shared MULTIPLE (≥).

Trap

Computing the wrong one.

Fix

Decide which the problem needs first.

05 / QUIZ

Test yourself.

The Test

12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.

0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).
Core

Core (4)

C1

You want to split 24 pens and 36 pencils into identical packs with none left over, using the largest pack size. Do you use the GCF or the LCM?

Need a hint?
  • Equal groups / simplify → GCF.
  • Line up / common denominator → LCM.
C2

Two buses leave together; one every 12 min, one every 18 min. To find when they next leave together, do you use the GCF or the LCM?

Need a hint?
  • Equal groups / simplify → GCF.
  • Line up / common denominator → LCM.
C3

Two buses leave together; one every 12 min, one every 18 min. To find when they next leave together, do you use the GCF or the LCM?

Need a hint?
  • Equal groups / simplify → GCF.
  • Line up / common denominator → LCM.
C4

Two buses leave together; one every 12 min, one every 18 min. To find when they next leave together, do you use the GCF or the LCM?

Need a hint?
  • Equal groups / simplify → GCF.
  • Line up / common denominator → LCM.
Apply

Apply (4)

A1

Two buses leave together; one every 12 min, one every 18 min. To find when they next leave together, do you use the GCF or the LCM?

Need a hint?
  • Equal groups / simplify → GCF.
  • Line up / common denominator → LCM.
A2

Two buses leave together; one every 12 min, one every 18 min. To find when they next leave together, do you use the GCF or the LCM?

Need a hint?
  • Equal groups / simplify → GCF.
  • Line up / common denominator → LCM.
A3

You want to split 24 pens and 36 pencils into identical packs with none left over, using the largest pack size. Do you use the GCF or the LCM?

Need a hint?
  • Equal groups / simplify → GCF.
  • Line up / common denominator → LCM.
A4

Two buses leave together; one every 12 min, one every 18 min. To find when they next leave together, do you use the GCF or the LCM?

Need a hint?
  • Equal groups / simplify → GCF.
  • Line up / common denominator → LCM.
Extension

Extension (4)

E1

Two buses leave together; one every 12 min, one every 18 min. To find when they next leave together, do you use the GCF or the LCM?

Need a hint?
  • Equal groups / simplify → GCF.
  • Line up / common denominator → LCM.
E2

Two buses leave together; one every 12 min, one every 18 min. To find when they next leave together, do you use the GCF or the LCM?

Need a hint?
  • Equal groups / simplify → GCF.
  • Line up / common denominator → LCM.
E3

You want to split 24 pens and 36 pencils into identical packs with none left over, using the largest pack size. Do you use the GCF or the LCM?

Need a hint?
  • Equal groups / simplify → GCF.
  • Line up / common denominator → LCM.
E4

You want to split 24 pens and 36 pencils into identical packs with none left over, using the largest pack size. Do you use the GCF or the LCM?

Need a hint?
  • Equal groups / simplify → GCF.
  • Line up / common denominator → LCM.