Least Common Multiple (LCM) of 23 and 189
The least common multiple (LCM) of 23 and 189 is 4347.
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 23 and 189?
First, calculate the GCD of 23 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 23 ÷ 189 = 0 remainder 23 |
| 2 | 189 ÷ 23 = 8 remainder 5 |
| 3 | 23 ÷ 5 = 4 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 174 and 16 | 1392 |
| 126 and 132 | 2772 |
| 174 and 38 | 3306 |
| 117 and 63 | 819 |
| 196 and 118 | 11564 |