Least Common Multiple (LCM) of 75 and 200
The least common multiple (LCM) of 75 and 200 is 600.
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 75 and 200?
First, calculate the GCD of 75 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 200 = 0 remainder 75 |
| 2 | 200 ÷ 75 = 2 remainder 50 |
| 3 | 75 ÷ 50 = 1 remainder 25 |
| 4 | 50 ÷ 25 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 71 and 80 | 5680 |
| 141 and 141 | 141 |
| 134 and 187 | 25058 |
| 186 and 108 | 3348 |
| 152 and 59 | 8968 |