Least Common Multiple (LCM) of 133 and 184
The least common multiple (LCM) of 133 and 184 is 24472.
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 184?
First, calculate the GCD of 133 and 184 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 133 ÷ 184 = 0 remainder 133 |
| 2 | 184 ÷ 133 = 1 remainder 51 |
| 3 | 133 ÷ 51 = 2 remainder 31 |
| 4 | 51 ÷ 31 = 1 remainder 20 |
| 5 | 31 ÷ 20 = 1 remainder 11 |
| 6 | 20 ÷ 11 = 1 remainder 9 |
| 7 | 11 ÷ 9 = 1 remainder 2 |
| 8 | 9 ÷ 2 = 4 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 67 | 7839 |
| 181 and 72 | 13032 |
| 73 and 109 | 7957 |
| 84 and 75 | 2100 |
| 177 and 191 | 33807 |