Least Common Multiple (LCM) of 200 and 109
The least common multiple (LCM) of 200 and 109 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 200 and 109?
First, calculate the GCD of 200 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 200 ÷ 109 = 1 remainder 91 |
| 2 | 109 ÷ 91 = 1 remainder 18 |
| 3 | 91 ÷ 18 = 5 remainder 1 |
| 4 | 18 ÷ 1 = 18 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 61 and 42 | 2562 |
| 32 and 48 | 96 |
| 126 and 185 | 23310 |
| 15 and 69 | 345 |
| 157 and 64 | 10048 |