Least Common Multiple (LCM) of 83 and 107
The least common multiple (LCM) of 83 and 107 is 8881.
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 83 and 107?
First, calculate the GCD of 83 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 107 = 0 remainder 83 |
| 2 | 107 ÷ 83 = 1 remainder 24 |
| 3 | 83 ÷ 24 = 3 remainder 11 |
| 4 | 24 ÷ 11 = 2 remainder 2 |
| 5 | 11 ÷ 2 = 5 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 15 | 30 |
| 129 and 136 | 17544 |
| 190 and 43 | 8170 |
| 39 and 24 | 312 |
| 85 and 43 | 3655 |