Least Common Multiple (LCM) of 163 and 108
The least common multiple (LCM) of 163 and 108 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 163 and 108?
First, calculate the GCD of 163 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 163 ÷ 108 = 1 remainder 55 |
| 2 | 108 ÷ 55 = 1 remainder 53 |
| 3 | 55 ÷ 53 = 1 remainder 2 |
| 4 | 53 ÷ 2 = 26 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 54 and 27 | 54 |
| 76 and 36 | 684 |
| 159 and 83 | 13197 |
| 137 and 143 | 19591 |
| 186 and 198 | 6138 |