Least Common Multiple (LCM) of 135 and 193
The least common multiple (LCM) of 135 and 193 is 26055.
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 193?
First, calculate the GCD of 135 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 193 = 0 remainder 135 |
| 2 | 193 ÷ 135 = 1 remainder 58 |
| 3 | 135 ÷ 58 = 2 remainder 19 |
| 4 | 58 ÷ 19 = 3 remainder 1 |
| 5 | 19 ÷ 1 = 19 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 152 and 132 | 5016 |
| 157 and 195 | 30615 |
| 127 and 127 | 127 |
| 10 and 130 | 130 |
| 40 and 73 | 2920 |