Least Common Multiple (LCM) of 200 and 115
The least common multiple (LCM) of 200 and 115 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 200 and 115?
First, calculate the GCD of 200 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 200 ÷ 115 = 1 remainder 85 |
| 2 | 115 ÷ 85 = 1 remainder 30 |
| 3 | 85 ÷ 30 = 2 remainder 25 |
| 4 | 30 ÷ 25 = 1 remainder 5 |
| 5 | 25 ÷ 5 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 85 | 510 |
| 144 and 178 | 12816 |
| 164 and 90 | 7380 |
| 192 and 75 | 4800 |
| 18 and 122 | 1098 |