Least Common Multiple (LCM) of 189 and 193
The least common multiple (LCM) of 189 and 193 is 36477.
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 193?
First, calculate the GCD of 189 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 193 = 0 remainder 189 |
| 2 | 193 ÷ 189 = 1 remainder 4 |
| 3 | 189 ÷ 4 = 47 remainder 1 |
| 4 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 63 | 8190 |
| 117 and 172 | 20124 |
| 11 and 64 | 704 |
| 63 and 117 | 819 |
| 115 and 118 | 13570 |