Least Common Multiple (LCM) of 86 and 180
The least common multiple (LCM) of 86 and 180 is 7740.
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 180?
First, calculate the GCD of 86 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 86 ÷ 180 = 0 remainder 86 |
| 2 | 180 ÷ 86 = 2 remainder 8 |
| 3 | 86 ÷ 8 = 10 remainder 6 |
| 4 | 8 ÷ 6 = 1 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 129 | 4644 |
| 92 and 37 | 3404 |
| 198 and 195 | 12870 |
| 67 and 136 | 9112 |
| 171 and 189 | 3591 |