Least Common Multiple (LCM) of 116 and 89
The least common multiple (LCM) of 116 and 89 is 10324.
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 116 and 89?
First, calculate the GCD of 116 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 89 = 1 remainder 27 |
| 2 | 89 ÷ 27 = 3 remainder 8 |
| 3 | 27 ÷ 8 = 3 remainder 3 |
| 4 | 8 ÷ 3 = 2 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 156 and 186 | 4836 |
| 60 and 10 | 60 |
| 145 and 53 | 7685 |
| 65 and 78 | 390 |
| 22 and 28 | 308 |