Least Common Multiple (LCM) of 86 and 111
The least common multiple (LCM) of 86 and 111 is 9546.
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 86 and 111?
First, calculate the GCD of 86 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 86 ÷ 111 = 0 remainder 86 |
| 2 | 111 ÷ 86 = 1 remainder 25 |
| 3 | 86 ÷ 25 = 3 remainder 11 |
| 4 | 25 ÷ 11 = 2 remainder 3 |
| 5 | 11 ÷ 3 = 3 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 27 and 129 | 1161 |
| 168 and 134 | 11256 |
| 172 and 154 | 13244 |
| 83 and 186 | 15438 |
| 141 and 155 | 21855 |