Least Common Multiple (LCM) of 193 and 107
The least common multiple (LCM) of 193 and 107 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 193 and 107?
First, calculate the GCD of 193 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 193 ÷ 107 = 1 remainder 86 |
| 2 | 107 ÷ 86 = 1 remainder 21 |
| 3 | 86 ÷ 21 = 4 remainder 2 |
| 4 | 21 ÷ 2 = 10 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 34 and 45 | 1530 |
| 197 and 81 | 15957 |
| 163 and 72 | 11736 |
| 105 and 16 | 1680 |
| 177 and 174 | 10266 |