Least Common Multiple (LCM) of 82 and 132
The least common multiple (LCM) of 82 and 132 is 5412.
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 132?
First, calculate the GCD of 82 and 132 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 132 = 0 remainder 82 |
| 2 | 132 ÷ 82 = 1 remainder 50 |
| 3 | 82 ÷ 50 = 1 remainder 32 |
| 4 | 50 ÷ 32 = 1 remainder 18 |
| 5 | 32 ÷ 18 = 1 remainder 14 |
| 6 | 18 ÷ 14 = 1 remainder 4 |
| 7 | 14 ÷ 4 = 3 remainder 2 |
| 8 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 159 and 196 | 31164 |
| 47 and 115 | 5405 |
| 84 and 173 | 14532 |
| 199 and 162 | 32238 |
| 170 and 150 | 2550 |