Least Common Multiple (LCM) of 133 and 180
The least common multiple (LCM) of 133 and 180 is 23940.
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 180?
First, calculate the GCD of 133 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 133 ÷ 180 = 0 remainder 133 |
| 2 | 180 ÷ 133 = 1 remainder 47 |
| 3 | 133 ÷ 47 = 2 remainder 39 |
| 4 | 47 ÷ 39 = 1 remainder 8 |
| 5 | 39 ÷ 8 = 4 remainder 7 |
| 6 | 8 ÷ 7 = 1 remainder 1 |
| 7 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 131 and 117 | 15327 |
| 154 and 132 | 924 |
| 42 and 67 | 2814 |
| 120 and 192 | 960 |
| 193 and 37 | 7141 |