Least Common Multiple (LCM) of 115 and 198
The least common multiple (LCM) of 115 and 198 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 115 and 198?
First, calculate the GCD of 115 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 198 = 0 remainder 115 |
| 2 | 198 ÷ 115 = 1 remainder 83 |
| 3 | 115 ÷ 83 = 1 remainder 32 |
| 4 | 83 ÷ 32 = 2 remainder 19 |
| 5 | 32 ÷ 19 = 1 remainder 13 |
| 6 | 19 ÷ 13 = 1 remainder 6 |
| 7 | 13 ÷ 6 = 2 remainder 1 |
| 8 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 54 and 131 | 7074 |
| 75 and 198 | 4950 |
| 23 and 200 | 4600 |
| 42 and 166 | 3486 |
| 127 and 173 | 21971 |