Least Common Multiple (LCM) of 127 and 200
The least common multiple (LCM) of 127 and 200 is 25400.
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 127 and 200?
First, calculate the GCD of 127 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 127 ÷ 200 = 0 remainder 127 |
| 2 | 200 ÷ 127 = 1 remainder 73 |
| 3 | 127 ÷ 73 = 1 remainder 54 |
| 4 | 73 ÷ 54 = 1 remainder 19 |
| 5 | 54 ÷ 19 = 2 remainder 16 |
| 6 | 19 ÷ 16 = 1 remainder 3 |
| 7 | 16 ÷ 3 = 5 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 29 | 580 |
| 193 and 157 | 30301 |
| 55 and 68 | 3740 |
| 71 and 118 | 8378 |
| 175 and 126 | 3150 |