Least Common Multiple (LCM) of 197 and 43
The least common multiple (LCM) of 197 and 43 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 197 and 43?
First, calculate the GCD of 197 and 43 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 197 ÷ 43 = 4 remainder 25 |
| 2 | 43 ÷ 25 = 1 remainder 18 |
| 3 | 25 ÷ 18 = 1 remainder 7 |
| 4 | 18 ÷ 7 = 2 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 118 | 13334 |
| 188 and 189 | 35532 |
| 141 and 186 | 8742 |
| 153 and 38 | 5814 |
| 189 and 39 | 2457 |