Least Common Multiple (LCM) of 12 and 25
The least common multiple (LCM) of 12 and 25 is 300.
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 25?
First, calculate the GCD of 12 and 25 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 12 ÷ 25 = 0 remainder 12 |
| 2 | 25 ÷ 12 = 2 remainder 1 |
| 3 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 194 | 4074 |
| 129 and 100 | 12900 |
| 117 and 48 | 1872 |
| 107 and 14 | 1498 |
| 199 and 159 | 31641 |