Least Common Multiple (LCM) of 110 and 190
The least common multiple (LCM) of 110 and 190 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 190?
First, calculate the GCD of 110 and 190 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 190 = 0 remainder 110 |
| 2 | 190 ÷ 110 = 1 remainder 80 |
| 3 | 110 ÷ 80 = 1 remainder 30 |
| 4 | 80 ÷ 30 = 2 remainder 20 |
| 5 | 30 ÷ 20 = 1 remainder 10 |
| 6 | 20 ÷ 10 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 62 and 65 | 4030 |
| 47 and 171 | 8037 |
| 90 and 101 | 9090 |
| 15 and 178 | 2670 |
| 189 and 190 | 35910 |