Least Common Multiple (LCM) of 19 and 110
The least common multiple (LCM) of 19 and 110 is 2090.
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 19 and 110?
First, calculate the GCD of 19 and 110 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 19 ÷ 110 = 0 remainder 19 |
| 2 | 110 ÷ 19 = 5 remainder 15 |
| 3 | 19 ÷ 15 = 1 remainder 4 |
| 4 | 15 ÷ 4 = 3 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 111 | 8880 |
| 60 and 35 | 420 |
| 72 and 189 | 1512 |
| 163 and 65 | 10595 |
| 195 and 57 | 3705 |