Least Common Multiple (LCM) of 200 and 118
The least common multiple (LCM) of 200 and 118 is 11800.
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 118?
First, calculate the GCD of 200 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 200 ÷ 118 = 1 remainder 82 |
| 2 | 118 ÷ 82 = 1 remainder 36 |
| 3 | 82 ÷ 36 = 2 remainder 10 |
| 4 | 36 ÷ 10 = 3 remainder 6 |
| 5 | 10 ÷ 6 = 1 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 187 and 180 | 33660 |
| 109 and 105 | 11445 |
| 193 and 141 | 27213 |
| 186 and 142 | 13206 |
| 49 and 102 | 4998 |