Least Common Multiple (LCM) of 200 and 125
The least common multiple (LCM) of 200 and 125 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 200 and 125?
First, calculate the GCD of 200 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 200 ÷ 125 = 1 remainder 75 |
| 2 | 125 ÷ 75 = 1 remainder 50 |
| 3 | 75 ÷ 50 = 1 remainder 25 |
| 4 | 50 ÷ 25 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 156 | 6708 |
| 188 and 69 | 12972 |
| 198 and 12 | 396 |
| 186 and 124 | 372 |
| 120 and 168 | 840 |