Least Common Multiple (LCM) of 197 and 45
The least common multiple (LCM) of 197 and 45 is 8865.
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 45?
First, calculate the GCD of 197 and 45 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 197 ÷ 45 = 4 remainder 17 |
| 2 | 45 ÷ 17 = 2 remainder 11 |
| 3 | 17 ÷ 11 = 1 remainder 6 |
| 4 | 11 ÷ 6 = 1 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 83 and 169 | 14027 |
| 59 and 119 | 7021 |
| 41 and 117 | 4797 |
| 125 and 100 | 500 |
| 65 and 33 | 2145 |