Least Common Multiple (LCM) of 23 and 197
The least common multiple (LCM) of 23 and 197 is 4531.
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 197?
First, calculate the GCD of 23 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 23 ÷ 197 = 0 remainder 23 |
| 2 | 197 ÷ 23 = 8 remainder 13 |
| 3 | 23 ÷ 13 = 1 remainder 10 |
| 4 | 13 ÷ 10 = 1 remainder 3 |
| 5 | 10 ÷ 3 = 3 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 178 | 9790 |
| 165 and 57 | 3135 |
| 22 and 181 | 3982 |
| 132 and 24 | 264 |
| 97 and 110 | 10670 |