Least Common Multiple (LCM) of 107 and 199
The least common multiple (LCM) of 107 and 199 is 21293.
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 199?
First, calculate the GCD of 107 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 199 = 0 remainder 107 |
| 2 | 199 ÷ 107 = 1 remainder 92 |
| 3 | 107 ÷ 92 = 1 remainder 15 |
| 4 | 92 ÷ 15 = 6 remainder 2 |
| 5 | 15 ÷ 2 = 7 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 143 and 182 | 2002 |
| 142 and 175 | 24850 |
| 193 and 126 | 24318 |
| 114 and 106 | 6042 |
| 184 and 44 | 2024 |