Least Common Multiple (LCM) of 189 and 197
The least common multiple (LCM) of 189 and 197 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 189 and 197?
First, calculate the GCD of 189 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 197 = 0 remainder 189 |
| 2 | 197 ÷ 189 = 1 remainder 8 |
| 3 | 189 ÷ 8 = 23 remainder 5 |
| 4 | 8 ÷ 5 = 1 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 53 and 157 | 8321 |
| 66 and 88 | 264 |
| 105 and 134 | 14070 |
| 78 and 181 | 14118 |
| 194 and 107 | 20758 |