Least Common Multiple (LCM) of 133 and 193
The least common multiple (LCM) of 133 and 193 is 25669.
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 193?
First, calculate the GCD of 133 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 133 ÷ 193 = 0 remainder 133 |
| 2 | 193 ÷ 133 = 1 remainder 60 |
| 3 | 133 ÷ 60 = 2 remainder 13 |
| 4 | 60 ÷ 13 = 4 remainder 8 |
| 5 | 13 ÷ 8 = 1 remainder 5 |
| 6 | 8 ÷ 5 = 1 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 122 | 20130 |
| 199 and 84 | 16716 |
| 145 and 170 | 4930 |
| 138 and 173 | 23874 |
| 107 and 54 | 5778 |