Least Common Multiple (LCM) of 199 and 43
The least common multiple (LCM) of 199 and 43 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 199 and 43?
First, calculate the GCD of 199 and 43 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 43 = 4 remainder 27 |
| 2 | 43 ÷ 27 = 1 remainder 16 |
| 3 | 27 ÷ 16 = 1 remainder 11 |
| 4 | 16 ÷ 11 = 1 remainder 5 |
| 5 | 11 ÷ 5 = 2 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 99 and 45 | 495 |
| 108 and 128 | 3456 |
| 128 and 116 | 3712 |
| 116 and 52 | 1508 |
| 20 and 134 | 1340 |