The L.C.M. – Least Common Multiple
Have you ever needed to find a number that is a multiple of two or more numbers?
In math, this is called the L.C.M., which means Least Common Multiple.
What is the L.C.M.?
The least common multiple of two or more numbers is the smallest number, greater than zero, that is a multiple of all those numbers.
In other words:
The L.C.M. is the first number you find in the list of common multiples.
Example:
Let’s find the L.C.M. of 4 and 6.
- Multiples of 4: 4, 8, 12, 16, 20, 24, 28...
- Multiples of 6: 6, 12, 18, 24, 30...
The common multiples are: 12, 24...
👉 The smallest one is 12
✅ So: L.C.M.(4, 6) = 12
What is it used for?
The L.C.M. is useful when we need to:
- Do operations with fractions, to find a common denominator
- Solve problems with different repeating rhythms (like two events happening at regular intervals)
- Organize objects or activities with different timings
How do you calculate the L.C.M.?
Method 1: Using multiples
- Write the multiples of each number
- Find the common ones
- Choose the smallest
✅ Good for small numbers.
Method 2: Using prime factorization
- Break down each number into prime factors
- Take all the factors, using the highest exponent for each
- Multiply them together
Example:
Find the L.C.M. of 12 and 18
- 12 = 2² × 3
- 18 = 2 × 3²
- L.C.M. = 2² × 3² = 36
Difference between L.C.M. and G.C.D.
| Abbreviation | Meaning | It is the... |
|---|---|---|
| L.C.M. | Least Common Multiple | smallest common multiple |
| G.C.D. | Greatest Common Divisor | largest common divisor |
Quick exercise
Find the L.C.M. of 8 and 10:
- Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80...
- Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80...
👉 Answer: 40
