Least Common Multiple (LCM) of 199 and 192
The least common multiple (LCM) of 199 and 192 is 38208.
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 192?
First, calculate the GCD of 199 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 192 = 1 remainder 7 |
| 2 | 192 ÷ 7 = 27 remainder 3 |
| 3 | 7 ÷ 3 = 2 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 173 | 22317 |
| 45 and 73 | 3285 |
| 12 and 135 | 540 |
| 189 and 57 | 3591 |
| 192 and 105 | 6720 |