Least Common Multiple (LCM) of 38 and 189
The least common multiple (LCM) of 38 and 189 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 38 and 189?
First, calculate the GCD of 38 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 38 ÷ 189 = 0 remainder 38 |
| 2 | 189 ÷ 38 = 4 remainder 37 |
| 3 | 38 ÷ 37 = 1 remainder 1 |
| 4 | 37 ÷ 1 = 37 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 60 and 115 | 1380 |
| 110 and 149 | 16390 |
| 49 and 182 | 1274 |
| 166 and 17 | 2822 |
| 194 and 85 | 16490 |