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 |
|---|---|
| 131 and 32 | 4192 |
| 150 and 186 | 4650 |
| 101 and 45 | 4545 |
| 51 and 197 | 10047 |
| 15 and 53 | 795 |