Least Common Multiple Calculator
Find the least common multiple (LCM) of two or more numbers, or the least common denominator (LCD) of fractions, with prime-factor steps.
Change the values and press Calculate to work out your own figures.
LCM of two or more numbers
Enter two or more numbers to find the smallest number they all divide into.
Show the working
- 15 = 3 × 5
- 25 = 5²
- 30 = 2 × 3 × 5
- Take each prime at its highest power: 2 × 3 × 5² = 150
- 150 ÷ 15 = 10
- 150 ÷ 25 = 6
- 150 ÷ 30 = 5
Least common denominator of fractions
Enter fractions or mixed numbers to find their least common denominator and rewrite each one over it.
| Fraction | Denominator | Multiply top and bottom | Equivalent fraction |
|---|---|---|---|
| 1/2 | 2 | × 6 | 6/12 |
| 3/4 | 4 | × 3 | 9/12 |
| 1 2/3 | 3 | × 4 | 20/12 |
Show the working
- The LCD is the least common multiple of the denominators 2, 4, 3: 12
- 12 ÷ 2 = 6
- 12 ÷ 4 = 3
- 12 ÷ 3 = 4
How to use it
Enter two or more numbers to find the smallest number they all divide into. Enter fractions or mixed numbers to find their least common denominator and rewrite each one over it.
The answer is exact: whole numbers of any size up to 30 digits are handled without rounding, and Show the working lists every step.
Key facts
LCM(a, b) = a × b ÷ GCF(a, b) LCD of fractions = LCM of their denominators
Finding the LCM with primes
Break each number into primes, then multiply every prime at the highest power it appears in any of the numbers. For 15 = 3 × 5, 25 = 5² and 30 = 2 × 3 × 5, that is 2 × 3 × 5² = 150.
Common denominators
To add or compare fractions, rewrite them over a common denominator. The least common denominator is the LCM of the denominators, which keeps the numbers as small as possible.
Questions
What is the LCM of 4 and 6?
12: it is the smallest number both 4 and 6 divide into.
What is the LCD of 1/2, 3/4 and 1 2/3?
12, the LCM of the denominators 2, 4 and 3.
Formulas
LCM(a, b) = a × b ÷ GCF(a, b) LCD of fractions = LCM of their denominators
Sources
Limitations
- Numbers have at most 30 digits; factor lists and prime factorizations are limited to 10¹².