Least Common Multiple (LCM) of 82 and 156
The least common multiple (LCM) of 82 and 156 is 6396.
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 156?
First, calculate the GCD of 82 and 156 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 156 = 0 remainder 82 |
| 2 | 156 ÷ 82 = 1 remainder 74 |
| 3 | 82 ÷ 74 = 1 remainder 8 |
| 4 | 74 ÷ 8 = 9 remainder 2 |
| 5 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 18 and 153 | 306 |
| 117 and 14 | 1638 |
| 33 and 73 | 2409 |
| 20 and 105 | 420 |
| 196 and 50 | 4900 |