Least Common Multiple (LCM) of 125 and 193
The least common multiple (LCM) of 125 and 193 is 24125.
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 125 and 193?
First, calculate the GCD of 125 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 125 ÷ 193 = 0 remainder 125 |
| 2 | 193 ÷ 125 = 1 remainder 68 |
| 3 | 125 ÷ 68 = 1 remainder 57 |
| 4 | 68 ÷ 57 = 1 remainder 11 |
| 5 | 57 ÷ 11 = 5 remainder 2 |
| 6 | 11 ÷ 2 = 5 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 193 | 20458 |
| 162 and 78 | 2106 |
| 60 and 117 | 2340 |
| 177 and 102 | 6018 |
| 49 and 131 | 6419 |