Least Common Multiple (LCM) of 82 and 46
The least common multiple (LCM) of 82 and 46 is 1886.
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 46?
First, calculate the GCD of 82 and 46 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 46 = 1 remainder 36 |
| 2 | 46 ÷ 36 = 1 remainder 10 |
| 3 | 36 ÷ 10 = 3 remainder 6 |
| 4 | 10 ÷ 6 = 1 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 119 and 74 | 8806 |
| 50 and 64 | 1600 |
| 160 and 34 | 2720 |
| 57 and 42 | 798 |
| 148 and 177 | 26196 |