Least Common Multiple (LCM) of 82 and 101
The least common multiple (LCM) of 82 and 101 is 8282.
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 101?
First, calculate the GCD of 82 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 101 = 0 remainder 82 |
| 2 | 101 ÷ 82 = 1 remainder 19 |
| 3 | 82 ÷ 19 = 4 remainder 6 |
| 4 | 19 ÷ 6 = 3 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 172 | 32508 |
| 83 and 43 | 3569 |
| 184 and 136 | 3128 |
| 192 and 45 | 2880 |
| 85 and 144 | 12240 |