Least Common Multiple (LCM) of 109 and 200
The least common multiple (LCM) of 109 and 200 is 21800.
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 109 and 200?
First, calculate the GCD of 109 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 200 = 0 remainder 109 |
| 2 | 200 ÷ 109 = 1 remainder 91 |
| 3 | 109 ÷ 91 = 1 remainder 18 |
| 4 | 91 ÷ 18 = 5 remainder 1 |
| 5 | 18 ÷ 1 = 18 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 90 and 91 | 8190 |
| 187 and 200 | 37400 |
| 42 and 190 | 3990 |
| 14 and 22 | 154 |
| 61 and 108 | 6588 |