Least Common Multiple (LCM) of 198 and 103
The least common multiple (LCM) of 198 and 103 is 20394.
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 198 and 103?
First, calculate the GCD of 198 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 198 ÷ 103 = 1 remainder 95 |
| 2 | 103 ÷ 95 = 1 remainder 8 |
| 3 | 95 ÷ 8 = 11 remainder 7 |
| 4 | 8 ÷ 7 = 1 remainder 1 |
| 5 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 136 and 45 | 6120 |
| 59 and 95 | 5605 |
| 120 and 200 | 600 |
| 187 and 82 | 15334 |
| 53 and 84 | 4452 |