Least Common Multiple (LCM) of 86 and 108
The least common multiple (LCM) of 86 and 108 is 4644.
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 108?
First, calculate the GCD of 86 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 86 ÷ 108 = 0 remainder 86 |
| 2 | 108 ÷ 86 = 1 remainder 22 |
| 3 | 86 ÷ 22 = 3 remainder 20 |
| 4 | 22 ÷ 20 = 1 remainder 2 |
| 5 | 20 ÷ 2 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 25 | 3550 |
| 169 and 79 | 13351 |
| 97 and 109 | 10573 |
| 101 and 82 | 8282 |
| 180 and 152 | 6840 |