Least Common Multiple (LCM) of 103 and 198
The least common multiple (LCM) of 103 and 198 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 103 and 198?
First, calculate the GCD of 103 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 198 = 0 remainder 103 |
| 2 | 198 ÷ 103 = 1 remainder 95 |
| 3 | 103 ÷ 95 = 1 remainder 8 |
| 4 | 95 ÷ 8 = 11 remainder 7 |
| 5 | 8 ÷ 7 = 1 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 19 | 2470 |
| 60 and 130 | 780 |
| 114 and 147 | 5586 |
| 19 and 132 | 2508 |
| 193 and 16 | 3088 |