Least Common Multiple (LCM) of 102 and 199
The least common multiple (LCM) of 102 and 199 is 20298.
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 102 and 199?
First, calculate the GCD of 102 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 199 = 0 remainder 102 |
| 2 | 199 ÷ 102 = 1 remainder 97 |
| 3 | 102 ÷ 97 = 1 remainder 5 |
| 4 | 97 ÷ 5 = 19 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 107 | 14445 |
| 19 and 83 | 1577 |
| 194 and 10 | 970 |
| 88 and 191 | 16808 |
| 57 and 29 | 1653 |