Least Common Multiple (LCM) of 199 and 111
The least common multiple (LCM) of 199 and 111 is 22089.
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 199 and 111?
First, calculate the GCD of 199 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 111 = 1 remainder 88 |
| 2 | 111 ÷ 88 = 1 remainder 23 |
| 3 | 88 ÷ 23 = 3 remainder 19 |
| 4 | 23 ÷ 19 = 1 remainder 4 |
| 5 | 19 ÷ 4 = 4 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 172 | 23564 |
| 22 and 135 | 2970 |
| 191 and 143 | 27313 |
| 16 and 73 | 1168 |
| 155 and 124 | 620 |