Least Common Multiple (LCM) of 189 and 30
The least common multiple (LCM) of 189 and 30 is 1890.
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 30?
First, calculate the GCD of 189 and 30 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 30 = 6 remainder 9 |
| 2 | 30 ÷ 9 = 3 remainder 3 |
| 3 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 173 | 20241 |
| 33 and 183 | 2013 |
| 197 and 73 | 14381 |
| 102 and 180 | 3060 |
| 29 and 183 | 5307 |