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 |
|---|---|
| 199 and 135 | 26865 |
| 199 and 98 | 19502 |
| 11 and 75 | 825 |
| 53 and 149 | 7897 |
| 199 and 132 | 26268 |