Least Common Multiple (LCM) of 83 and 108
The least common multiple (LCM) of 83 and 108 is 8964.
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 108?
First, calculate the GCD of 83 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 108 = 0 remainder 83 |
| 2 | 108 ÷ 83 = 1 remainder 25 |
| 3 | 83 ÷ 25 = 3 remainder 8 |
| 4 | 25 ÷ 8 = 3 remainder 1 |
| 5 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 108 | 7236 |
| 28 and 119 | 476 |
| 86 and 12 | 516 |
| 141 and 83 | 11703 |
| 172 and 105 | 18060 |