Least Common Multiple (LCM) of 113 and 200
The least common multiple (LCM) of 113 and 200 is 22600.
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 113 and 200?
First, calculate the GCD of 113 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 200 = 0 remainder 113 |
| 2 | 200 ÷ 113 = 1 remainder 87 |
| 3 | 113 ÷ 87 = 1 remainder 26 |
| 4 | 87 ÷ 26 = 3 remainder 9 |
| 5 | 26 ÷ 9 = 2 remainder 8 |
| 6 | 9 ÷ 8 = 1 remainder 1 |
| 7 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 51 and 24 | 408 |
| 108 and 129 | 4644 |
| 100 and 142 | 7100 |
| 51 and 181 | 9231 |
| 184 and 87 | 16008 |