Least Common Multiple (LCM) of 66 and 89
The least common multiple (LCM) of 66 and 89 is 5874.
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 66 and 89?
First, calculate the GCD of 66 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 66 ÷ 89 = 0 remainder 66 |
| 2 | 89 ÷ 66 = 1 remainder 23 |
| 3 | 66 ÷ 23 = 2 remainder 20 |
| 4 | 23 ÷ 20 = 1 remainder 3 |
| 5 | 20 ÷ 3 = 6 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 11 and 189 | 2079 |
| 29 and 148 | 4292 |
| 105 and 45 | 315 |
| 104 and 149 | 15496 |
| 122 and 130 | 7930 |