Least Common Multiple (LCM) of 110 and 19
The least common multiple (LCM) of 110 and 19 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 110 and 19?
First, calculate the GCD of 110 and 19 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 19 = 5 remainder 15 |
| 2 | 19 ÷ 15 = 1 remainder 4 |
| 3 | 15 ÷ 4 = 3 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 125 and 160 | 4000 |
| 185 and 11 | 2035 |
| 12 and 15 | 60 |
| 56 and 20 | 280 |
| 108 and 107 | 11556 |