Least Common Multiple (LCM) of 199 and 110
The least common multiple (LCM) of 199 and 110 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 199 and 110?
First, calculate the GCD of 199 and 110 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 110 = 1 remainder 89 |
| 2 | 110 ÷ 89 = 1 remainder 21 |
| 3 | 89 ÷ 21 = 4 remainder 5 |
| 4 | 21 ÷ 5 = 4 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 185 and 59 | 10915 |
| 15 and 79 | 1185 |
| 172 and 164 | 7052 |
| 132 and 70 | 4620 |
| 77 and 131 | 10087 |