Least Common Multiple (LCM) of 180 and 133
The least common multiple (LCM) of 180 and 133 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 180 and 133?
First, calculate the GCD of 180 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 133 = 1 remainder 47 |
| 2 | 133 ÷ 47 = 2 remainder 39 |
| 3 | 47 ÷ 39 = 1 remainder 8 |
| 4 | 39 ÷ 8 = 4 remainder 7 |
| 5 | 8 ÷ 7 = 1 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 198 and 85 | 16830 |
| 183 and 179 | 32757 |
| 144 and 195 | 9360 |
| 77 and 177 | 13629 |
| 112 and 161 | 2576 |