Least Common Multiple (LCM) of 135 and 171
The least common multiple (LCM) of 135 and 171 is 2565.
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 171?
First, calculate the GCD of 135 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 171 = 0 remainder 135 |
| 2 | 171 ÷ 135 = 1 remainder 36 |
| 3 | 135 ÷ 36 = 3 remainder 27 |
| 4 | 36 ÷ 27 = 1 remainder 9 |
| 5 | 27 ÷ 9 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 43 | 8256 |
| 54 and 102 | 918 |
| 66 and 183 | 4026 |
| 21 and 158 | 3318 |
| 60 and 72 | 360 |