Least Common Multiple (LCM) of 198 and 115
The least common multiple (LCM) of 198 and 115 is 22770.
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 115?
First, calculate the GCD of 198 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 198 ÷ 115 = 1 remainder 83 |
| 2 | 115 ÷ 83 = 1 remainder 32 |
| 3 | 83 ÷ 32 = 2 remainder 19 |
| 4 | 32 ÷ 19 = 1 remainder 13 |
| 5 | 19 ÷ 13 = 1 remainder 6 |
| 6 | 13 ÷ 6 = 2 remainder 1 |
| 7 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 143 and 10 | 1430 |
| 194 and 40 | 3880 |
| 136 and 46 | 3128 |
| 22 and 12 | 132 |
| 132 and 63 | 2772 |