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 |
|---|---|
| 170 and 175 | 5950 |
| 11 and 119 | 1309 |
| 33 and 55 | 165 |
| 80 and 151 | 12080 |
| 85 and 61 | 5185 |