Least Common Multiple (LCM) of 198 and 71
The least common multiple (LCM) of 198 and 71 is 14058.
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 71?
First, calculate the GCD of 198 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 198 ÷ 71 = 2 remainder 56 |
| 2 | 71 ÷ 56 = 1 remainder 15 |
| 3 | 56 ÷ 15 = 3 remainder 11 |
| 4 | 15 ÷ 11 = 1 remainder 4 |
| 5 | 11 ÷ 4 = 2 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 54 | 378 |
| 192 and 133 | 25536 |
| 31 and 52 | 1612 |
| 79 and 79 | 79 |
| 103 and 133 | 13699 |