Least Common Multiple (LCM) of 197 and 189
The least common multiple (LCM) of 197 and 189 is 37233.
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 197 and 189?
First, calculate the GCD of 197 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 197 ÷ 189 = 1 remainder 8 |
| 2 | 189 ÷ 8 = 23 remainder 5 |
| 3 | 8 ÷ 5 = 1 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 |
|---|---|
| 18 and 90 | 90 |
| 63 and 43 | 2709 |
| 62 and 85 | 5270 |
| 127 and 47 | 5969 |
| 136 and 189 | 25704 |