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 |
|---|---|
| 128 and 76 | 2432 |
| 121 and 57 | 6897 |
| 106 and 59 | 6254 |
| 190 and 84 | 7980 |
| 130 and 116 | 7540 |