Least Common Multiple (LCM) of 189 and 97
The least common multiple (LCM) of 189 and 97 is 18333.
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 97?
First, calculate the GCD of 189 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 97 = 1 remainder 92 |
| 2 | 97 ÷ 92 = 1 remainder 5 |
| 3 | 92 ÷ 5 = 18 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 154 and 142 | 10934 |
| 183 and 162 | 9882 |
| 123 and 52 | 6396 |
| 199 and 191 | 38009 |
| 93 and 25 | 2325 |