Least Common Multiple (LCM) of 135 and 163
The least common multiple (LCM) of 135 and 163 is 22005.
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 163?
First, calculate the GCD of 135 and 163 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 163 = 0 remainder 135 |
| 2 | 163 ÷ 135 = 1 remainder 28 |
| 3 | 135 ÷ 28 = 4 remainder 23 |
| 4 | 28 ÷ 23 = 1 remainder 5 |
| 5 | 23 ÷ 5 = 4 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 55 and 172 | 9460 |
| 29 and 177 | 5133 |
| 189 and 86 | 16254 |
| 71 and 151 | 10721 |
| 112 and 183 | 20496 |