Least Common Multiple (LCM) of 133 and 60
The least common multiple (LCM) of 133 and 60 is 7980.
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 60?
First, calculate the GCD of 133 and 60 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 133 ÷ 60 = 2 remainder 13 |
| 2 | 60 ÷ 13 = 4 remainder 8 |
| 3 | 13 ÷ 8 = 1 remainder 5 |
| 4 | 8 ÷ 5 = 1 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 29 and 180 | 5220 |
| 149 and 125 | 18625 |
| 63 and 132 | 2772 |
| 54 and 21 | 378 |
| 90 and 81 | 810 |