Least Common Multiple (LCM) of 133 and 103
The least common multiple (LCM) of 133 and 103 is 13699.
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 103?
First, calculate the GCD of 133 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 133 ÷ 103 = 1 remainder 30 |
| 2 | 103 ÷ 30 = 3 remainder 13 |
| 3 | 30 ÷ 13 = 2 remainder 4 |
| 4 | 13 ÷ 4 = 3 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 141 and 197 | 27777 |
| 119 and 64 | 7616 |
| 10 and 45 | 90 |
| 75 and 87 | 2175 |
| 158 and 115 | 18170 |