Least Common Multiple (LCM) of 12 and 125
The least common multiple (LCM) of 12 and 125 is 1500.
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 12 and 125?
First, calculate the GCD of 12 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 12 ÷ 125 = 0 remainder 12 |
| 2 | 125 ÷ 12 = 10 remainder 5 |
| 3 | 12 ÷ 5 = 2 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 168 and 84 | 168 |
| 135 and 45 | 135 |
| 149 and 142 | 21158 |
| 147 and 22 | 3234 |
| 24 and 78 | 312 |