Least Common Multiple (LCM) of 111 and 198
The least common multiple (LCM) of 111 and 198 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 111 and 198?
First, calculate the GCD of 111 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 198 = 0 remainder 111 |
| 2 | 198 ÷ 111 = 1 remainder 87 |
| 3 | 111 ÷ 87 = 1 remainder 24 |
| 4 | 87 ÷ 24 = 3 remainder 15 |
| 5 | 24 ÷ 15 = 1 remainder 9 |
| 6 | 15 ÷ 9 = 1 remainder 6 |
| 7 | 9 ÷ 6 = 1 remainder 3 |
| 8 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 60 and 71 | 4260 |
| 90 and 111 | 3330 |
| 105 and 110 | 2310 |
| 125 and 176 | 22000 |
| 11 and 145 | 1595 |