Least Common Multiple (LCM) of 12 and 27
The least common multiple (LCM) of 12 and 27 is 108.
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 27?
First, calculate the GCD of 12 and 27 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 12 ÷ 27 = 0 remainder 12 |
| 2 | 27 ÷ 12 = 2 remainder 3 |
| 3 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 129 | 1935 |
| 58 and 186 | 5394 |
| 161 and 104 | 16744 |
| 27 and 173 | 4671 |
| 110 and 32 | 1760 |