Least Common Multiple (LCM) of 137 and 193
The least common multiple (LCM) of 137 and 193 is 26441.
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 137 and 193?
First, calculate the GCD of 137 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 193 = 0 remainder 137 |
| 2 | 193 ÷ 137 = 1 remainder 56 |
| 3 | 137 ÷ 56 = 2 remainder 25 |
| 4 | 56 ÷ 25 = 2 remainder 6 |
| 5 | 25 ÷ 6 = 4 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 82 and 174 | 7134 |
| 198 and 107 | 21186 |
| 26 and 176 | 2288 |
| 183 and 146 | 26718 |
| 45 and 118 | 5310 |