Least Common Multiple (LCM) of 111 and 107
The least common multiple (LCM) of 111 and 107 is 11877.
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 111 and 107?
First, calculate the GCD of 111 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 107 = 1 remainder 4 |
| 2 | 107 ÷ 4 = 26 remainder 3 |
| 3 | 4 ÷ 3 = 1 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 182 and 105 | 2730 |
| 99 and 146 | 14454 |
| 181 and 110 | 19910 |
| 148 and 30 | 2220 |
| 27 and 72 | 216 |