Least Common Multiple (LCM) of 43 and 82
The least common multiple (LCM) of 43 and 82 is 3526.
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 43 and 82?
First, calculate the GCD of 43 and 82 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 43 ÷ 82 = 0 remainder 43 |
| 2 | 82 ÷ 43 = 1 remainder 39 |
| 3 | 43 ÷ 39 = 1 remainder 4 |
| 4 | 39 ÷ 4 = 9 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 156 and 169 | 2028 |
| 62 and 142 | 4402 |
| 137 and 66 | 9042 |
| 155 and 98 | 15190 |
| 138 and 172 | 11868 |