Least Common Multiple (LCM) of 111 and 200
The least common multiple (LCM) of 111 and 200 is 22200.
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 200?
First, calculate the GCD of 111 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 200 = 0 remainder 111 |
| 2 | 200 ÷ 111 = 1 remainder 89 |
| 3 | 111 ÷ 89 = 1 remainder 22 |
| 4 | 89 ÷ 22 = 4 remainder 1 |
| 5 | 22 ÷ 1 = 22 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 178 | 29370 |
| 125 and 148 | 18500 |
| 180 and 76 | 3420 |
| 104 and 98 | 5096 |
| 114 and 174 | 3306 |