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 |
|---|---|
| 156 and 47 | 7332 |
| 10 and 153 | 1530 |
| 56 and 153 | 8568 |
| 32 and 180 | 1440 |
| 108 and 164 | 4428 |