Least Common Multiple (LCM) of 200 and 45
The least common multiple (LCM) of 200 and 45 is 1800.
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 45?
First, calculate the GCD of 200 and 45 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 200 ÷ 45 = 4 remainder 20 |
| 2 | 45 ÷ 20 = 2 remainder 5 |
| 3 | 20 ÷ 5 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 16 and 178 | 1424 |
| 149 and 132 | 19668 |
| 66 and 63 | 1386 |
| 102 and 15 | 510 |
| 198 and 102 | 3366 |