Least Common Multiple (LCM) of 133 and 107
The least common multiple (LCM) of 133 and 107 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 133 and 107?
First, calculate the GCD of 133 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 133 ÷ 107 = 1 remainder 26 |
| 2 | 107 ÷ 26 = 4 remainder 3 |
| 3 | 26 ÷ 3 = 8 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 50 and 23 | 1150 |
| 181 and 28 | 5068 |
| 169 and 92 | 15548 |
| 133 and 113 | 15029 |
| 91 and 20 | 1820 |