Least Common Multiple (LCM) of 138 and 193
The least common multiple (LCM) of 138 and 193 is 26634.
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 138 and 193?
First, calculate the GCD of 138 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 193 = 0 remainder 138 |
| 2 | 193 ÷ 138 = 1 remainder 55 |
| 3 | 138 ÷ 55 = 2 remainder 28 |
| 4 | 55 ÷ 28 = 1 remainder 27 |
| 5 | 28 ÷ 27 = 1 remainder 1 |
| 6 | 27 ÷ 1 = 27 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 155 and 40 | 1240 |
| 198 and 114 | 3762 |
| 74 and 138 | 5106 |
| 129 and 99 | 4257 |
| 188 and 23 | 4324 |