Least Common Multiple (LCM) of 199 and 47
The least common multiple (LCM) of 199 and 47 is 9353.
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 47?
First, calculate the GCD of 199 and 47 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 47 = 4 remainder 11 |
| 2 | 47 ÷ 11 = 4 remainder 3 |
| 3 | 11 ÷ 3 = 3 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 168 and 199 | 33432 |
| 172 and 35 | 6020 |
| 174 and 45 | 2610 |
| 108 and 52 | 1404 |
| 126 and 192 | 4032 |