Least Common Multiple (LCM) of 108 and 83
The least common multiple (LCM) of 108 and 83 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 108 and 83?
First, calculate the GCD of 108 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 83 = 1 remainder 25 |
| 2 | 83 ÷ 25 = 3 remainder 8 |
| 3 | 25 ÷ 8 = 3 remainder 1 |
| 4 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 133 and 65 | 8645 |
| 97 and 15 | 1455 |
| 17 and 92 | 1564 |
| 149 and 51 | 7599 |
| 97 and 52 | 5044 |