Least Common Multiple (LCM) of 200 and 142
The least common multiple (LCM) of 200 and 142 is 14200.
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 200 and 142?
First, calculate the GCD of 200 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 200 ÷ 142 = 1 remainder 58 |
| 2 | 142 ÷ 58 = 2 remainder 26 |
| 3 | 58 ÷ 26 = 2 remainder 6 |
| 4 | 26 ÷ 6 = 4 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 77 and 69 | 5313 |
| 110 and 15 | 330 |
| 11 and 123 | 1353 |
| 150 and 100 | 300 |
| 137 and 183 | 25071 |