Least Common Multiple (LCM) of 89 and 66
The least common multiple (LCM) of 89 and 66 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 89 and 66?
First, calculate the GCD of 89 and 66 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 66 = 1 remainder 23 |
| 2 | 66 ÷ 23 = 2 remainder 20 |
| 3 | 23 ÷ 20 = 1 remainder 3 |
| 4 | 20 ÷ 3 = 6 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 196 and 39 | 7644 |
| 150 and 15 | 150 |
| 141 and 18 | 846 |
| 141 and 173 | 24393 |
| 145 and 45 | 1305 |