Least Common Multiple
Find the Least Common Multiple (LCM) of two numbers
"Least Common Multiple" Calculator
How to find the LCM of 6 and 8
The least common multiple (LCM) of two numbers is the smallest natural number that both of them divide.
6 = 2 × 3
8 = 23
| Prime | 6 | 8 | Highest power |
|---|---|---|---|
| 2 | 2 | 23 | 23 |
| 3 | 3 | — | 3 |
— = power 0: the prime is not a factor of this number; the LCM takes it from the number that has it.
LCM = 23 × 3 = 24
Rule: factor each number into primes; the LCM multiplies every prime that appears, each at its highest power.
See Also
- Greatest Common Factor - Find the Greatest Common Factor (GCF) of two numbers
- Least Common Multiple of 3 Numbers - Find the Least Common Multiple (LCM) of three numbers
- Greatest Common Factor of 3 Numbers - Find the Greatest Common Factor (GCF) of three numbers
- Multiples of a Number - List the first 10 multiples of any number from 1 to 999
FAQ
What is the least common multiple of two numbers?
It is the smallest positive integer that both numbers divide into without a remainder. Multiples of 6 are 6, 12, 18, 24…, multiples of 8 are 8, 16, 24…, and 24 is the first value on both lists, so the LCM of 6 and 8 is 24. Every pair has one, because the product of the two numbers is already a common multiple.
How do you calculate the LCM without listing multiples?
Two standard routes. By prime factorization, take each prime to the highest power it reaches in either number: 12 = 2² × 3 and 16 = 2⁴, so the LCM is 2⁴ × 3 = 48. Or go through the greatest common divisor, since LCM(a, b) = a × b ÷ GCD(a, b) — for 12 and 16 that is 12 × 16 ÷ 4 = 48.
Why is the LCM used as the common denominator of fractions?
Adding fractions needs a single denominator that both original denominators divide into, and the least common multiple is the smallest one available, so the numbers stay manageable. For 1/6 + 1/8 the LCM of 6 and 8 is 24: 1/6 becomes 4/24, 1/8 becomes 3/24, and the sum is 7/24.