Least Common Multiple (LCM) of 199 and 107
The least common multiple (LCM) of 199 and 107 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 199 and 107?
First, calculate the GCD of 199 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 107 = 1 remainder 92 |
| 2 | 107 ÷ 92 = 1 remainder 15 |
| 3 | 92 ÷ 15 = 6 remainder 2 |
| 4 | 15 ÷ 2 = 7 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 157 | 2198 |
| 163 and 16 | 2608 |
| 59 and 195 | 11505 |
| 94 and 120 | 5640 |
| 165 and 172 | 28380 |