Least Common Multiple (LCM) of 80 and 125
The least common multiple (LCM) of 80 and 125 is 2000.
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 80 and 125?
First, calculate the GCD of 80 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 80 ÷ 125 = 0 remainder 80 |
| 2 | 125 ÷ 80 = 1 remainder 45 |
| 3 | 80 ÷ 45 = 1 remainder 35 |
| 4 | 45 ÷ 35 = 1 remainder 10 |
| 5 | 35 ÷ 10 = 3 remainder 5 |
| 6 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 29 | 4785 |
| 119 and 123 | 14637 |
| 14 and 66 | 462 |
| 10 and 96 | 480 |
| 85 and 73 | 6205 |