Least Common Multiple (LCM) of 43 and 198
The least common multiple (LCM) of 43 and 198 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 43 and 198?
First, calculate the GCD of 43 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 43 ÷ 198 = 0 remainder 43 |
| 2 | 198 ÷ 43 = 4 remainder 26 |
| 3 | 43 ÷ 26 = 1 remainder 17 |
| 4 | 26 ÷ 17 = 1 remainder 9 |
| 5 | 17 ÷ 9 = 1 remainder 8 |
| 6 | 9 ÷ 8 = 1 remainder 1 |
| 7 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 133 and 33 | 4389 |
| 180 and 92 | 4140 |
| 176 and 121 | 1936 |
| 73 and 15 | 1095 |
| 111 and 68 | 7548 |