Least Common Multiple (LCM) of 133 and 45
The least common multiple (LCM) of 133 and 45 is 5985.
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 45?
First, calculate the GCD of 133 and 45 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 133 ÷ 45 = 2 remainder 43 |
| 2 | 45 ÷ 43 = 1 remainder 2 |
| 3 | 43 ÷ 2 = 21 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 82 | 5248 |
| 188 and 81 | 15228 |
| 107 and 166 | 17762 |
| 36 and 90 | 180 |
| 62 and 170 | 5270 |