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 |
|---|---|
| 159 and 63 | 3339 |
| 110 and 157 | 17270 |
| 82 and 145 | 11890 |
| 148 and 83 | 12284 |
| 37 and 112 | 4144 |