Least Common Multiple (LCM) of 198 and 43
The least common multiple (LCM) of 198 and 43 is 8514.
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 198 and 43?
First, calculate the GCD of 198 and 43 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 198 ÷ 43 = 4 remainder 26 |
| 2 | 43 ÷ 26 = 1 remainder 17 |
| 3 | 26 ÷ 17 = 1 remainder 9 |
| 4 | 17 ÷ 9 = 1 remainder 8 |
| 5 | 9 ÷ 8 = 1 remainder 1 |
| 6 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 11 and 54 | 594 |
| 108 and 83 | 8964 |
| 172 and 181 | 31132 |
| 183 and 109 | 19947 |
| 186 and 57 | 3534 |