Least Common Multiple (LCM) of 43 and 197
The least common multiple (LCM) of 43 and 197 is 8471.
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 43 and 197?
First, calculate the GCD of 43 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 43 ÷ 197 = 0 remainder 43 |
| 2 | 197 ÷ 43 = 4 remainder 25 |
| 3 | 43 ÷ 25 = 1 remainder 18 |
| 4 | 25 ÷ 18 = 1 remainder 7 |
| 5 | 18 ÷ 7 = 2 remainder 4 |
| 6 | 7 ÷ 4 = 1 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 124 and 135 | 16740 |
| 24 and 16 | 48 |
| 51 and 158 | 8058 |
| 153 and 191 | 29223 |
| 129 and 70 | 9030 |