Least Common Multiple (LCM) of 189 and 38
The least common multiple (LCM) of 189 and 38 is 7182.
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 38?
First, calculate the GCD of 189 and 38 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 38 = 4 remainder 37 |
| 2 | 38 ÷ 37 = 1 remainder 1 |
| 3 | 37 ÷ 1 = 37 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 60 and 109 | 6540 |
| 80 and 17 | 1360 |
| 135 and 195 | 1755 |
| 190 and 81 | 15390 |
| 131 and 24 | 3144 |