Least Common Multiple (LCM) of 82 and 30
The least common multiple (LCM) of 82 and 30 is 1230.
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 30?
First, calculate the GCD of 82 and 30 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 30 = 2 remainder 22 |
| 2 | 30 ÷ 22 = 1 remainder 8 |
| 3 | 22 ÷ 8 = 2 remainder 6 |
| 4 | 8 ÷ 6 = 1 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 72 and 110 | 3960 |
| 196 and 101 | 19796 |
| 196 and 97 | 19012 |
| 100 and 161 | 16100 |
| 70 and 105 | 210 |