Least Common Multiple (LCM) of 133 and 178
The least common multiple (LCM) of 133 and 178 is 23674.
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 178?
First, calculate the GCD of 133 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 133 ÷ 178 = 0 remainder 133 |
| 2 | 178 ÷ 133 = 1 remainder 45 |
| 3 | 133 ÷ 45 = 2 remainder 43 |
| 4 | 45 ÷ 43 = 1 remainder 2 |
| 5 | 43 ÷ 2 = 21 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 65 and 192 | 12480 |
| 169 and 107 | 18083 |
| 155 and 47 | 7285 |
| 104 and 121 | 12584 |
| 154 and 83 | 12782 |