Least Common Multiple (LCM) of 199 and 102
The least common multiple (LCM) of 199 and 102 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 199 and 102?
First, calculate the GCD of 199 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 102 = 1 remainder 97 |
| 2 | 102 ÷ 97 = 1 remainder 5 |
| 3 | 97 ÷ 5 = 19 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 194 and 137 | 26578 |
| 43 and 100 | 4300 |
| 128 and 184 | 2944 |
| 52 and 144 | 1872 |
| 112 and 21 | 336 |