Least Common Multiple (LCM) of 133 and 176
The least common multiple (LCM) of 133 and 176 is 23408.
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 176?
First, calculate the GCD of 133 and 176 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 133 ÷ 176 = 0 remainder 133 |
| 2 | 176 ÷ 133 = 1 remainder 43 |
| 3 | 133 ÷ 43 = 3 remainder 4 |
| 4 | 43 ÷ 4 = 10 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 42 | 672 |
| 132 and 149 | 19668 |
| 189 and 76 | 14364 |
| 123 and 49 | 6027 |
| 102 and 125 | 12750 |