Least Common Multiple (LCM) of 189 and 57
The least common multiple (LCM) of 189 and 57 is 3591.
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 57?
First, calculate the GCD of 189 and 57 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 57 = 3 remainder 18 |
| 2 | 57 ÷ 18 = 3 remainder 3 |
| 3 | 18 ÷ 3 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 84 and 156 | 1092 |
| 168 and 100 | 4200 |
| 150 and 100 | 300 |
| 14 and 70 | 70 |
| 134 and 67 | 134 |