Least Common Multiple (LCM) of 110 and 199
The least common multiple (LCM) of 110 and 199 is 21890.
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 110 and 199?
First, calculate the GCD of 110 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 199 = 0 remainder 110 |
| 2 | 199 ÷ 110 = 1 remainder 89 |
| 3 | 110 ÷ 89 = 1 remainder 21 |
| 4 | 89 ÷ 21 = 4 remainder 5 |
| 5 | 21 ÷ 5 = 4 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 54 and 154 | 4158 |
| 144 and 177 | 8496 |
| 198 and 197 | 39006 |
| 153 and 143 | 21879 |
| 165 and 163 | 26895 |