LCM of 7 and 9 with Working
The LCM of 7 and 9 (least common multiple) is 63. 63 = 3² × 7, and the greatest common factor (HCF) of 7 and 9 is 1. 7 and 9 are coprime, so the LCM is their product.
63 ÷ 7 = 9 · 63 ÷ 9 = 7 · GCF = 1
Open 7 and 9 in the calculator
How to find the LCM of 7 and 9: six methods
Every method below reaches 63. Pick the one your class uses; the working is the same as the calculator shows.
Listing multiples: LCM of 7 and 9
Listing multiples: LCM(7, 9)
Write out the multiples of each number until one multiple appears in every row. The first number that appears in all rows is the least common multiple.
63 is the first multiple shared by every number.
LCM(7, 9) = 63
Prime factorization: LCM of 7 and 9
Prime factorization: LCM(7, 9)
Break each number into prime factors.
- 7 = 7
- 9 = 3 × 3 = 3²
Take the highest power of every prime that appears, then multiply them together.
| Prime | Highest power | From |
|---|---|---|
| 3 | 3² | 9 |
| 7 | 7 | 7 |
LCM = 3² × 7 = 63
LCM(7, 9) = 63
Cake (ladder) method: LCM of 7 and 9
Cake (ladder) method: LCM(7, 9)
The cake (ladder) method divides the numbers by a prime shared by at least two of them. Here no prime is shared by two numbers, so the LCM is simply the numbers multiplied together.
LCM = 7 × 9 = 63
LCM(7, 9) = 63
Division method: LCM of 7 and 9
Division method: LCM(7, 9)
Divide the row by the smallest prime that goes into at least one number; carry the rest down. Keep going until every number becomes 1. The LCM is the product of all the divisors on the left.
| 3 | 7 | 9 |
|---|---|---|
| 3 | 7 | 3 |
| 7 | 7 | 1 |
| 1 | 1 |
LCM = 3 × 3 × 7 = 3² × 7 = 63
LCM(7, 9) = 63
Using the GCF: LCM of 7 and 9
Using the GCF: LCM(7, 9)
For two numbers, LCM(a, b) = a × b ÷ GCF(a, b).
- GCF(7, 9) = 1, so LCM(7, 9) = 7 × 9 ÷ 1 = 63 ÷ 1 = 63
LCM(7, 9) = 63
Venn diagram: LCM of 7 and 9
Venn diagram: LCM(7, 9)
Put each number's prime factors in its circle. Factors shared by two (or three) numbers go where the circles overlap, written once. Multiply every factor in the diagram to get the LCM; the overlap alone gives the GCF.
LCM = 7 × 3 × 3 = 63
GCF = 1 = 1
LCM(7, 9) = 63
Facts about 7 and 9
- Prime factorization: 7 = 7; 9 = 3².
- GCF (HCF) of 7 and 9: 1. LCM × GCF = 63 = 7 × 9.
- First three common multiples of 7 and 9: 63, 126, 189.
- 7 and 9 are coprime (no shared prime factor).
Nearby pairs
- LCM of 6 and 9 = 18
- LCM of 9 and 12 = 36
- LCM of 6 and 7 = 42
- LCM of 7 and 8 = 56
- LCM of 8 and 9 = 72
Frequently asked questions
What is the LCM of 7 and 9?
The LCM of 7 and 9 is 63. 63 is the smallest positive number that both 7 and 9 divide into exactly: 63 ÷ 7 = 9 and 63 ÷ 9 = 7.
What is the GCF of 7 and 9?
The GCF (HCF) of 7 and 9 is 1. Check: LCM × GCF = 63 × 1 = 63 = 7 × 9.
How do you find the LCM of 7 and 9?
Prime factorization: 7 = 7 and 9 = 3². Take each prime at its highest power: 3² × 7 = 63.
Sources
- Wikipedia: Least common multiple: definition, notation, LCM × GCD = a × b
- Wolfram MathWorld: Least Common Multiple: formal properties
- Common Core 6.NS.B.4: GCF and LCM in grade 6