Least Common Multiple (LCM) of 200 and 126
The least common multiple (LCM) of 200 and 126 is 12600.
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 126?
First, calculate the GCD of 200 and 126 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 200 ÷ 126 = 1 remainder 74 |
| 2 | 126 ÷ 74 = 1 remainder 52 |
| 3 | 74 ÷ 52 = 1 remainder 22 |
| 4 | 52 ÷ 22 = 2 remainder 8 |
| 5 | 22 ÷ 8 = 2 remainder 6 |
| 6 | 8 ÷ 6 = 1 remainder 2 |
| 7 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 180 | 5760 |
| 46 and 165 | 7590 |
| 37 and 37 | 37 |
| 19 and 83 | 1577 |
| 54 and 20 | 540 |