Least Common Multiple (LCM) of 115 and 200
The least common multiple (LCM) of 115 and 200 is 4600.
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 115 and 200?
First, calculate the GCD of 115 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 200 = 0 remainder 115 |
| 2 | 200 ÷ 115 = 1 remainder 85 |
| 3 | 115 ÷ 85 = 1 remainder 30 |
| 4 | 85 ÷ 30 = 2 remainder 25 |
| 5 | 30 ÷ 25 = 1 remainder 5 |
| 6 | 25 ÷ 5 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 36 and 191 | 6876 |
| 114 and 121 | 13794 |
| 189 and 74 | 13986 |
| 22 and 119 | 2618 |
| 151 and 102 | 15402 |