Least Common Multiple (LCM) of 200 and 54
The least common multiple (LCM) of 200 and 54 is 5400.
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 54?
First, calculate the GCD of 200 and 54 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 200 ÷ 54 = 3 remainder 38 |
| 2 | 54 ÷ 38 = 1 remainder 16 |
| 3 | 38 ÷ 16 = 2 remainder 6 |
| 4 | 16 ÷ 6 = 2 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 10 | 1170 |
| 199 and 33 | 6567 |
| 165 and 150 | 1650 |
| 30 and 50 | 150 |
| 134 and 131 | 17554 |