Least Common Multiple (LCM) of 199 and 14
The least common multiple (LCM) of 199 and 14 is 2786.
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 14?
First, calculate the GCD of 199 and 14 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 14 = 14 remainder 3 |
| 2 | 14 ÷ 3 = 4 remainder 2 |
| 3 | 3 ÷ 2 = 1 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 186 | 11346 |
| 198 and 106 | 10494 |
| 141 and 147 | 6909 |
| 164 and 197 | 32308 |
| 171 and 100 | 17100 |