Least Common Multiple (LCM) of 16 and 199
The least common multiple (LCM) of 16 and 199 is 3184.
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 16 and 199?
First, calculate the GCD of 16 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 16 ÷ 199 = 0 remainder 16 |
| 2 | 199 ÷ 16 = 12 remainder 7 |
| 3 | 16 ÷ 7 = 2 remainder 2 |
| 4 | 7 ÷ 2 = 3 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 197 and 152 | 29944 |
| 109 and 108 | 11772 |
| 55 and 110 | 110 |
| 183 and 82 | 15006 |
| 196 and 114 | 11172 |