Least Common Multiple (LCM) of 127 and 193
The least common multiple (LCM) of 127 and 193 is 24511.
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 127 and 193?
First, calculate the GCD of 127 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 127 ÷ 193 = 0 remainder 127 |
| 2 | 193 ÷ 127 = 1 remainder 66 |
| 3 | 127 ÷ 66 = 1 remainder 61 |
| 4 | 66 ÷ 61 = 1 remainder 5 |
| 5 | 61 ÷ 5 = 12 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 197 and 34 | 6698 |
| 25 and 112 | 2800 |
| 25 and 12 | 300 |
| 52 and 30 | 780 |
| 80 and 174 | 6960 |