Least Common Multiple (LCM) of 198 and 142
The least common multiple (LCM) of 198 and 142 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 142?
First, calculate the GCD of 198 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 198 ÷ 142 = 1 remainder 56 |
| 2 | 142 ÷ 56 = 2 remainder 30 |
| 3 | 56 ÷ 30 = 1 remainder 26 |
| 4 | 30 ÷ 26 = 1 remainder 4 |
| 5 | 26 ÷ 4 = 6 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 64 and 170 | 5440 |
| 165 and 29 | 4785 |
| 55 and 20 | 220 |
| 58 and 81 | 4698 |
| 128 and 57 | 7296 |