Least Common Multiple (LCM) of 200 and 116
The least common multiple (LCM) of 200 and 116 is 5800.
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 116?
First, calculate the GCD of 200 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 200 ÷ 116 = 1 remainder 84 |
| 2 | 116 ÷ 84 = 1 remainder 32 |
| 3 | 84 ÷ 32 = 2 remainder 20 |
| 4 | 32 ÷ 20 = 1 remainder 12 |
| 5 | 20 ÷ 12 = 1 remainder 8 |
| 6 | 12 ÷ 8 = 1 remainder 4 |
| 7 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 99 and 189 | 2079 |
| 85 and 75 | 1275 |
| 131 and 46 | 6026 |
| 183 and 55 | 10065 |
| 160 and 63 | 10080 |