Least Common Multiple (LCM) of 133 and 163
The least common multiple (LCM) of 133 and 163 is 21679.
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 163?
First, calculate the GCD of 133 and 163 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 133 ÷ 163 = 0 remainder 133 |
| 2 | 163 ÷ 133 = 1 remainder 30 |
| 3 | 133 ÷ 30 = 4 remainder 13 |
| 4 | 30 ÷ 13 = 2 remainder 4 |
| 5 | 13 ÷ 4 = 3 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 111 and 171 | 6327 |
| 185 and 143 | 26455 |
| 46 and 57 | 2622 |
| 133 and 117 | 15561 |
| 126 and 180 | 1260 |