Least Common Multiple (LCM) of 126 and 200
The least common multiple (LCM) of 126 and 200 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 126 and 200?
First, calculate the GCD of 126 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 200 = 0 remainder 126 |
| 2 | 200 ÷ 126 = 1 remainder 74 |
| 3 | 126 ÷ 74 = 1 remainder 52 |
| 4 | 74 ÷ 52 = 1 remainder 22 |
| 5 | 52 ÷ 22 = 2 remainder 8 |
| 6 | 22 ÷ 8 = 2 remainder 6 |
| 7 | 8 ÷ 6 = 1 remainder 2 |
| 8 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 46 and 47 | 2162 |
| 100 and 55 | 1100 |
| 188 and 28 | 1316 |
| 139 and 165 | 22935 |
| 199 and 20 | 3980 |