Least Common Multiple (LCM) of 108 and 198
The least common multiple (LCM) of 108 and 198 is 1188.
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 108 and 198?
First, calculate the GCD of 108 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 198 = 0 remainder 108 |
| 2 | 198 ÷ 108 = 1 remainder 90 |
| 3 | 108 ÷ 90 = 1 remainder 18 |
| 4 | 90 ÷ 18 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 190 and 16 | 1520 |
| 130 and 140 | 1820 |
| 115 and 91 | 10465 |
| 14 and 48 | 336 |
| 135 and 119 | 16065 |