Least Common Multiple (LCM) of 38 and 199
The least common multiple (LCM) of 38 and 199 is 7562.
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 38 and 199?
First, calculate the GCD of 38 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 38 ÷ 199 = 0 remainder 38 |
| 2 | 199 ÷ 38 = 5 remainder 9 |
| 3 | 38 ÷ 9 = 4 remainder 2 |
| 4 | 9 ÷ 2 = 4 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 27 and 132 | 1188 |
| 14 and 57 | 798 |
| 197 and 31 | 6107 |
| 101 and 199 | 20099 |
| 180 and 120 | 360 |