Least Common Multiple (LCM) of 82 and 52
The least common multiple (LCM) of 82 and 52 is 2132.
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 52?
First, calculate the GCD of 82 and 52 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 52 = 1 remainder 30 |
| 2 | 52 ÷ 30 = 1 remainder 22 |
| 3 | 30 ÷ 22 = 1 remainder 8 |
| 4 | 22 ÷ 8 = 2 remainder 6 |
| 5 | 8 ÷ 6 = 1 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 101 and 119 | 12019 |
| 176 and 33 | 528 |
| 142 and 129 | 18318 |
| 60 and 18 | 180 |
| 68 and 34 | 68 |