Least Common Multiple (LCM) of 12 and 107
The least common multiple (LCM) of 12 and 107 is 1284.
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 107?
First, calculate the GCD of 12 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 12 ÷ 107 = 0 remainder 12 |
| 2 | 107 ÷ 12 = 8 remainder 11 |
| 3 | 12 ÷ 11 = 1 remainder 1 |
| 4 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 67 | 7705 |
| 189 and 121 | 22869 |
| 82 and 182 | 7462 |
| 185 and 170 | 6290 |
| 127 and 65 | 8255 |