Least Common Multiple (LCM) of 199 and 84
The least common multiple (LCM) of 199 and 84 is 16716.
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 84?
First, calculate the GCD of 199 and 84 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 84 = 2 remainder 31 |
| 2 | 84 ÷ 31 = 2 remainder 22 |
| 3 | 31 ÷ 22 = 1 remainder 9 |
| 4 | 22 ÷ 9 = 2 remainder 4 |
| 5 | 9 ÷ 4 = 2 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 160 | 160 |
| 119 and 85 | 595 |
| 117 and 59 | 6903 |
| 131 and 193 | 25283 |
| 113 and 51 | 5763 |