Least Common Multiple (LCM) of 198 and 111
The least common multiple (LCM) of 198 and 111 is 7326.
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 111?
First, calculate the GCD of 198 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 198 ÷ 111 = 1 remainder 87 |
| 2 | 111 ÷ 87 = 1 remainder 24 |
| 3 | 87 ÷ 24 = 3 remainder 15 |
| 4 | 24 ÷ 15 = 1 remainder 9 |
| 5 | 15 ÷ 9 = 1 remainder 6 |
| 6 | 9 ÷ 6 = 1 remainder 3 |
| 7 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 19 and 84 | 1596 |
| 195 and 73 | 14235 |
| 199 and 91 | 18109 |
| 68 and 44 | 748 |
| 157 and 192 | 30144 |