Least Common Multiple (LCM) of 109 and 89
The least common multiple (LCM) of 109 and 89 is 9701.
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 109 and 89?
First, calculate the GCD of 109 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 89 = 1 remainder 20 |
| 2 | 89 ÷ 20 = 4 remainder 9 |
| 3 | 20 ÷ 9 = 2 remainder 2 |
| 4 | 9 ÷ 2 = 4 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 179 | 17184 |
| 41 and 11 | 451 |
| 14 and 195 | 2730 |
| 141 and 34 | 4794 |
| 78 and 49 | 3822 |