Least Common Multiple (LCM) of 199 and 200
The least common multiple (LCM) of 199 and 200 is 39800.
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 200?
First, calculate the GCD of 199 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 200 = 0 remainder 199 |
| 2 | 200 ÷ 199 = 1 remainder 1 |
| 3 | 199 ÷ 1 = 199 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 51 and 87 | 1479 |
| 97 and 75 | 7275 |
| 74 and 20 | 740 |
| 173 and 171 | 29583 |
| 15 and 60 | 60 |