Least Common Multiple (LCM) of 43 and 199
The least common multiple (LCM) of 43 and 199 is 8557.
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 43 and 199?
First, calculate the GCD of 43 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 43 ÷ 199 = 0 remainder 43 |
| 2 | 199 ÷ 43 = 4 remainder 27 |
| 3 | 43 ÷ 27 = 1 remainder 16 |
| 4 | 27 ÷ 16 = 1 remainder 11 |
| 5 | 16 ÷ 11 = 1 remainder 5 |
| 6 | 11 ÷ 5 = 2 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 57 | 7410 |
| 46 and 46 | 46 |
| 17 and 147 | 2499 |
| 40 and 114 | 2280 |
| 164 and 14 | 1148 |