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 |
|---|---|
| 117 and 85 | 9945 |
| 166 and 195 | 32370 |
| 89 and 75 | 6675 |
| 69 and 114 | 2622 |
| 196 and 95 | 18620 |