Least Common Multiple (LCM) of 82 and 158
The least common multiple (LCM) of 82 and 158 is 6478.
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 158?
First, calculate the GCD of 82 and 158 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 158 = 0 remainder 82 |
| 2 | 158 ÷ 82 = 1 remainder 76 |
| 3 | 82 ÷ 76 = 1 remainder 6 |
| 4 | 76 ÷ 6 = 12 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 54 and 54 | 54 |
| 146 and 175 | 25550 |
| 105 and 112 | 1680 |
| 198 and 143 | 2574 |
| 51 and 61 | 3111 |