Least Common Multiple (LCM) of 67 and 86
The least common multiple (LCM) of 67 and 86 is 5762.
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 67 and 86?
First, calculate the GCD of 67 and 86 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 86 = 0 remainder 67 |
| 2 | 86 ÷ 67 = 1 remainder 19 |
| 3 | 67 ÷ 19 = 3 remainder 10 |
| 4 | 19 ÷ 10 = 1 remainder 9 |
| 5 | 10 ÷ 9 = 1 remainder 1 |
| 6 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 109 | 19075 |
| 134 and 86 | 5762 |
| 12 and 147 | 588 |
| 193 and 25 | 4825 |
| 66 and 129 | 2838 |