Least Common Multiple (LCM) of 199 and 39
The least common multiple (LCM) of 199 and 39 is 7761.
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 39?
First, calculate the GCD of 199 and 39 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 39 = 5 remainder 4 |
| 2 | 39 ÷ 4 = 9 remainder 3 |
| 3 | 4 ÷ 3 = 1 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 178 | 33642 |
| 99 and 140 | 13860 |
| 140 and 158 | 11060 |
| 16 and 161 | 2576 |
| 73 and 25 | 1825 |