Least Common Multiple (LCM) of 107 and 193
The least common multiple (LCM) of 107 and 193 is 20651.
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 107 and 193?
First, calculate the GCD of 107 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 193 = 0 remainder 107 |
| 2 | 193 ÷ 107 = 1 remainder 86 |
| 3 | 107 ÷ 86 = 1 remainder 21 |
| 4 | 86 ÷ 21 = 4 remainder 2 |
| 5 | 21 ÷ 2 = 10 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 18 | 1206 |
| 112 and 157 | 17584 |
| 75 and 83 | 6225 |
| 11 and 34 | 374 |
| 10 and 86 | 430 |