Least Common Multiple (LCM) of 135 and 12
The least common multiple (LCM) of 135 and 12 is 540.
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 135 and 12?
First, calculate the GCD of 135 and 12 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 12 = 11 remainder 3 |
| 2 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 172 | 23564 |
| 167 and 81 | 13527 |
| 100 and 16 | 400 |
| 158 and 159 | 25122 |
| 105 and 89 | 9345 |