Least Common Multiple (LCM) of 200 and 193
The least common multiple (LCM) of 200 and 193 is 38600.
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 193?
First, calculate the GCD of 200 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 200 ÷ 193 = 1 remainder 7 |
| 2 | 193 ÷ 7 = 27 remainder 4 |
| 3 | 7 ÷ 4 = 1 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 48 and 30 | 240 |
| 144 and 52 | 1872 |
| 74 and 106 | 3922 |
| 110 and 125 | 2750 |
| 108 and 38 | 2052 |