Least Common Multiple (LCM) of 110 and 111
The least common multiple (LCM) of 110 and 111 is 12210.
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 111?
First, calculate the GCD of 110 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 111 = 0 remainder 110 |
| 2 | 111 ÷ 110 = 1 remainder 1 |
| 3 | 110 ÷ 1 = 110 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 19 | 2090 |
| 15 and 55 | 165 |
| 187 and 171 | 31977 |
| 171 and 188 | 32148 |
| 101 and 12 | 1212 |