Least Common Multiple (LCM) of 108 and 163
The least common multiple (LCM) of 108 and 163 is 17604.
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 163?
First, calculate the GCD of 108 and 163 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 163 = 0 remainder 108 |
| 2 | 163 ÷ 108 = 1 remainder 55 |
| 3 | 108 ÷ 55 = 1 remainder 53 |
| 4 | 55 ÷ 53 = 1 remainder 2 |
| 5 | 53 ÷ 2 = 26 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 20 | 2180 |
| 149 and 31 | 4619 |
| 132 and 165 | 660 |
| 86 and 94 | 4042 |
| 174 and 140 | 12180 |