Least Common Multiple (LCM) of 198 and 118
The least common multiple (LCM) of 198 and 118 is 11682.
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 118?
First, calculate the GCD of 198 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 198 ÷ 118 = 1 remainder 80 |
| 2 | 118 ÷ 80 = 1 remainder 38 |
| 3 | 80 ÷ 38 = 2 remainder 4 |
| 4 | 38 ÷ 4 = 9 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 192 | 8640 |
| 70 and 165 | 2310 |
| 144 and 84 | 1008 |
| 90 and 194 | 8730 |
| 141 and 22 | 3102 |