PEAZIT Aha card
Go straight to resources ↓Common divisors and multiples: compare prime factors
The GCD takes shared prime factors with smaller exponents. The LCM must contain both factorisations, so it takes larger exponents.
| Expression | Meaning |
|---|---|
| 12 = 2² × 3; 18 = 2 × 3² | Write both prime factorisations. |
| 2 × 3 = 6 | GCD: one factor of 2 and one of 3 are shared. |
| 2² × 3² = 36 | LCM: two factors of 2 and two of 3 cover both originals. |
One worked example
- 12 = 2² × 3; 18 = 2 × 3²Write both prime factorisations.
- 2 × 3 = 6GCD: one factor of 2 and one of 3 are shared.
- 2² × 3² = 36LCM: two factors of 2 and two of 3 cover both originals.
Watch out: This method is used here for positive integers. The least common multiple sought is positive.
Goal, prerequisites and card origin
What you will learn: Find the greatest common divisor and least common multiple.
What you need first: Prime factorisation.
An original PEAZIT working card. Independent expert review and effectiveness testing have not yet taken place. · v1
Show connections
The GCD takes shared prime factors with smaller exponents. The LCM must contain both factorisations, so it takes larger exponents.