Least Common Multiple (LCM) of 180 and 163
The least common multiple (LCM) of 180 and 163 is 29340.
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 163?
First, calculate the GCD of 180 and 163 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 163 = 1 remainder 17 |
| 2 | 163 ÷ 17 = 9 remainder 10 |
| 3 | 17 ÷ 10 = 1 remainder 7 |
| 4 | 10 ÷ 7 = 1 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 179 | 20406 |
| 129 and 131 | 16899 |
| 133 and 21 | 399 |
| 166 and 177 | 29382 |
| 77 and 193 | 14861 |