Least Common Multiple (LCM) of 75 and 89
The least common multiple (LCM) of 75 and 89 is 6675.
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 75 and 89?
First, calculate the GCD of 75 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 89 = 0 remainder 75 |
| 2 | 89 ÷ 75 = 1 remainder 14 |
| 3 | 75 ÷ 14 = 5 remainder 5 |
| 4 | 14 ÷ 5 = 2 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 39 and 46 | 1794 |
| 26 and 185 | 4810 |
| 16 and 95 | 1520 |
| 14 and 23 | 322 |
| 46 and 46 | 46 |