Least Common Multiple (LCM) of 75 and 189
The least common multiple (LCM) of 75 and 189 is 4725.
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 189?
First, calculate the GCD of 75 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 189 = 0 remainder 75 |
| 2 | 189 ÷ 75 = 2 remainder 39 |
| 3 | 75 ÷ 39 = 1 remainder 36 |
| 4 | 39 ÷ 36 = 1 remainder 3 |
| 5 | 36 ÷ 3 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 29 and 200 | 5800 |
| 105 and 175 | 525 |
| 137 and 171 | 23427 |
| 175 and 126 | 3150 |
| 65 and 20 | 260 |