What is the least common multiple (LCM)?
The least common multiple is the smallest number that each of your numbers divides into exactly. People also call it the lowest common multiple. Finding it is part of grade 6 maths in the Common Core standards, and it is the common denominator you need when adding fractions.
Source Microsoft Support · LCM function (least common multiple), with examples ↗Common Core State Standards · Grade 6, The Number System (6.NS.B.4) ↗
How to calculate the LCM
The shortcut works for numbers of any size: multiply the numbers and divide by their greatest common factor. With three or more numbers, do it two at a time.
Here it is with your numbers:
- The GCF of 6 and 8 is 2.
- LCM(6, 8) = 6 × 8 ÷ 2
- LCM(6, 8) = 24
It means 24 is the first number that is in both the 6 times table and the 8 times table.
Source NIST · Dictionary of Algorithms and Data Structures: Euclid's algorithm ↗
Two ways to check it
Write out each times table until a number appears in all of them, or break each number into prime factors and multiply the highest power of each prime.
| Number | Multiples | Prime factors |
|---|---|---|
| 6 | 6, 12, 18, 24 | 2 × 3 |
| 8 | 8, 16, 24 | 2³ |
| LCM | 24 | 2³ × 3 |
LCM examples
FAQs
What is the least common multiple?
The least common multiple is the smallest positive whole number that is a multiple of every one of your numbers. For 24 and 36 it is 72. It is the common denominator you need to add fractions with different denominators.
Source Microsoft Support · LCM function (least common multiple), with examples ↗
How do you find the least common multiple?
Multiply the two numbers and divide by their greatest common factor. For 6 and 8: 6 × 8 is 48, their greatest common factor is 2, and 48 ÷ 2 is 24. For small numbers you can also write out each times table until a number appears in both.
Source NIST · Dictionary of Algorithms and Data Structures: Euclid's algorithm ↗
What are the least common multiples of 6 and 8?
The least common multiple of 6 and 8 is 24. The 6 times table goes 6, 12, 18, 24 and the 8 times table goes 8, 16, 24, so 24 is the first number in both.
Source Microsoft Support · LCM function (least common multiple), with examples ↗
Sources
- Microsoft Support: LCM function (least common multiple), with examples
- NIST: Dictionary of Algorithms and Data Structures: Euclid's algorithm
- Common Core State Standards: Grade 6, The Number System (6.NS.B.4)