Least Common Multiple (LCM) of 199 and 117
The least common multiple (LCM) of 199 and 117 is 23283.
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 117?
First, calculate the GCD of 199 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 117 = 1 remainder 82 |
| 2 | 117 ÷ 82 = 1 remainder 35 |
| 3 | 82 ÷ 35 = 2 remainder 12 |
| 4 | 35 ÷ 12 = 2 remainder 11 |
| 5 | 12 ÷ 11 = 1 remainder 1 |
| 6 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 104 and 32 | 416 |
| 189 and 125 | 23625 |
| 51 and 155 | 7905 |
| 41 and 68 | 2788 |
| 55 and 68 | 3740 |