Least Common Multiple (LCM) of 108 and 89
The least common multiple (LCM) of 108 and 89 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 108 and 89?
First, calculate the GCD of 108 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 89 = 1 remainder 19 |
| 2 | 89 ÷ 19 = 4 remainder 13 |
| 3 | 19 ÷ 13 = 1 remainder 6 |
| 4 | 13 ÷ 6 = 2 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 176 and 10 | 880 |
| 149 and 46 | 6854 |
| 69 and 124 | 8556 |
| 103 and 119 | 12257 |
| 123 and 190 | 23370 |