Least Common Multiple (LCM) of 200 and 57
The least common multiple (LCM) of 200 and 57 is 11400.
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 57?
First, calculate the GCD of 200 and 57 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 200 ÷ 57 = 3 remainder 29 |
| 2 | 57 ÷ 29 = 1 remainder 28 |
| 3 | 29 ÷ 28 = 1 remainder 1 |
| 4 | 28 ÷ 1 = 28 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 27 and 50 | 1350 |
| 42 and 175 | 1050 |
| 157 and 68 | 10676 |
| 149 and 141 | 21009 |
| 112 and 184 | 2576 |