Least Common Multiple (LCM) of 20 and 133
The least common multiple (LCM) of 20 and 133 is 2660.
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 20 and 133?
First, calculate the GCD of 20 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 20 ÷ 133 = 0 remainder 20 |
| 2 | 133 ÷ 20 = 6 remainder 13 |
| 3 | 20 ÷ 13 = 1 remainder 7 |
| 4 | 13 ÷ 7 = 1 remainder 6 |
| 5 | 7 ÷ 6 = 1 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 33 and 82 | 2706 |
| 142 and 155 | 22010 |
| 166 and 19 | 3154 |
| 199 and 22 | 4378 |
| 59 and 171 | 10089 |