Least Common Multiple (LCM) of 189 and 39
The least common multiple (LCM) of 189 and 39 is 2457.
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 39?
First, calculate the GCD of 189 and 39 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 39 = 4 remainder 33 |
| 2 | 39 ÷ 33 = 1 remainder 6 |
| 3 | 33 ÷ 6 = 5 remainder 3 |
| 4 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 121 and 27 | 3267 |
| 193 and 43 | 8299 |
| 160 and 180 | 1440 |
| 161 and 68 | 10948 |
| 174 and 112 | 9744 |