Least Common Multiple (LCM) of 107 and 133
The least common multiple (LCM) of 107 and 133 is 14231.
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 107 and 133?
First, calculate the GCD of 107 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 133 = 0 remainder 107 |
| 2 | 133 ÷ 107 = 1 remainder 26 |
| 3 | 107 ÷ 26 = 4 remainder 3 |
| 4 | 26 ÷ 3 = 8 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 49 and 51 | 2499 |
| 83 and 188 | 15604 |
| 108 and 179 | 19332 |
| 82 and 103 | 8446 |
| 60 and 85 | 1020 |