Least Common Multiple (LCM) of 125 and 200
The least common multiple (LCM) of 125 and 200 is 1000.
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 125 and 200?
First, calculate the GCD of 125 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 125 ÷ 200 = 0 remainder 125 |
| 2 | 200 ÷ 125 = 1 remainder 75 |
| 3 | 125 ÷ 75 = 1 remainder 50 |
| 4 | 75 ÷ 50 = 1 remainder 25 |
| 5 | 50 ÷ 25 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 158 and 100 | 7900 |
| 67 and 174 | 11658 |
| 119 and 75 | 8925 |
| 10 and 21 | 210 |
| 69 and 125 | 8625 |