Least Common Multiple (LCM) of 110 and 86
The least common multiple (LCM) of 110 and 86 is 4730.
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 86?
First, calculate the GCD of 110 and 86 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 86 = 1 remainder 24 |
| 2 | 86 ÷ 24 = 3 remainder 14 |
| 3 | 24 ÷ 14 = 1 remainder 10 |
| 4 | 14 ÷ 10 = 1 remainder 4 |
| 5 | 10 ÷ 4 = 2 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 14 | 938 |
| 192 and 82 | 7872 |
| 114 and 194 | 11058 |
| 71 and 167 | 11857 |
| 77 and 128 | 9856 |