Least Common Multiple (LCM) of 89 and 108
The least common multiple (LCM) of 89 and 108 is 9612.
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 89 and 108?
First, calculate the GCD of 89 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 108 = 0 remainder 89 |
| 2 | 108 ÷ 89 = 1 remainder 19 |
| 3 | 89 ÷ 19 = 4 remainder 13 |
| 4 | 19 ÷ 13 = 1 remainder 6 |
| 5 | 13 ÷ 6 = 2 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 10 and 102 | 510 |
| 53 and 171 | 9063 |
| 177 and 105 | 6195 |
| 96 and 46 | 2208 |
| 177 and 50 | 8850 |