Least Common Multiple (LCM) of 131 and 180
The least common multiple (LCM) of 131 and 180 is 23580.
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 131 and 180?
First, calculate the GCD of 131 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 131 ÷ 180 = 0 remainder 131 |
| 2 | 180 ÷ 131 = 1 remainder 49 |
| 3 | 131 ÷ 49 = 2 remainder 33 |
| 4 | 49 ÷ 33 = 1 remainder 16 |
| 5 | 33 ÷ 16 = 2 remainder 1 |
| 6 | 16 ÷ 1 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 161 | 4025 |
| 198 and 200 | 19800 |
| 151 and 23 | 3473 |
| 183 and 22 | 4026 |
| 63 and 195 | 4095 |