Least Common Multiple (LCM) of 135 and 200
The least common multiple (LCM) of 135 and 200 is 5400.
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 200?
First, calculate the GCD of 135 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 200 = 0 remainder 135 |
| 2 | 200 ÷ 135 = 1 remainder 65 |
| 3 | 135 ÷ 65 = 2 remainder 5 |
| 4 | 65 ÷ 5 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 195 | 1560 |
| 185 and 151 | 27935 |
| 116 and 183 | 21228 |
| 177 and 193 | 34161 |
| 102 and 189 | 6426 |