Least Common Multiple (LCM) of 189 and 75
The least common multiple (LCM) of 189 and 75 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 189 and 75?
First, calculate the GCD of 189 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 75 = 2 remainder 39 |
| 2 | 75 ÷ 39 = 1 remainder 36 |
| 3 | 39 ÷ 36 = 1 remainder 3 |
| 4 | 36 ÷ 3 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 13 and 110 | 1430 |
| 30 and 156 | 780 |
| 26 and 26 | 26 |
| 138 and 74 | 5106 |
| 12 and 125 | 1500 |