Least Common Multiple (LCM) of 45 and 197
The least common multiple (LCM) of 45 and 197 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 45 and 197?
First, calculate the GCD of 45 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 197 = 0 remainder 45 |
| 2 | 197 ÷ 45 = 4 remainder 17 |
| 3 | 45 ÷ 17 = 2 remainder 11 |
| 4 | 17 ÷ 11 = 1 remainder 6 |
| 5 | 11 ÷ 6 = 1 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 25 | 675 |
| 27 and 161 | 4347 |
| 110 and 120 | 1320 |
| 118 and 123 | 14514 |
| 165 and 119 | 19635 |