Least Common Multiple (LCM) of 200 and 73
The least common multiple (LCM) of 200 and 73 is 14600.
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 73?
First, calculate the GCD of 200 and 73 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 200 ÷ 73 = 2 remainder 54 |
| 2 | 73 ÷ 54 = 1 remainder 19 |
| 3 | 54 ÷ 19 = 2 remainder 16 |
| 4 | 19 ÷ 16 = 1 remainder 3 |
| 5 | 16 ÷ 3 = 5 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 31 | 4030 |
| 119 and 52 | 6188 |
| 92 and 15 | 1380 |
| 150 and 200 | 600 |
| 30 and 114 | 570 |