Least Common Multiple (LCM) of 82 and 87
The least common multiple (LCM) of 82 and 87 is 7134.
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 82 and 87?
First, calculate the GCD of 82 and 87 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 87 = 0 remainder 82 |
| 2 | 87 ÷ 82 = 1 remainder 5 |
| 3 | 82 ÷ 5 = 16 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 126 | 5166 |
| 42 and 104 | 2184 |
| 130 and 159 | 20670 |
| 125 and 195 | 4875 |
| 109 and 196 | 21364 |