Least Common Multiple (LCM) of 82 and 182
The least common multiple (LCM) of 82 and 182 is 7462.
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 182?
First, calculate the GCD of 82 and 182 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 182 = 0 remainder 82 |
| 2 | 182 ÷ 82 = 2 remainder 18 |
| 3 | 82 ÷ 18 = 4 remainder 10 |
| 4 | 18 ÷ 10 = 1 remainder 8 |
| 5 | 10 ÷ 8 = 1 remainder 2 |
| 6 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 154 and 57 | 8778 |
| 110 and 159 | 17490 |
| 147 and 78 | 3822 |
| 105 and 40 | 840 |
| 143 and 165 | 2145 |