Least Common Multiple (LCM) of 12 and 18
The least common multiple (LCM) of 12 and 18 is 36.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 12 and 18?
First, calculate the GCD of 12 and 18 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 12 ÷ 18 = 0 remainder 12 |
| 2 | 18 ÷ 12 = 1 remainder 6 |
| 3 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 171 and 139 | 23769 |
| 166 and 162 | 13446 |
| 39 and 78 | 78 |
| 165 and 170 | 5610 |
| 119 and 123 | 14637 |