Least Common Multiple (LCM) of 143 and 180
The least common multiple (LCM) of 143 and 180 is 25740.
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 143 and 180?
First, calculate the GCD of 143 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 143 ÷ 180 = 0 remainder 143 |
| 2 | 180 ÷ 143 = 1 remainder 37 |
| 3 | 143 ÷ 37 = 3 remainder 32 |
| 4 | 37 ÷ 32 = 1 remainder 5 |
| 5 | 32 ÷ 5 = 6 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 164 and 84 | 3444 |
| 89 and 106 | 9434 |
| 32 and 57 | 1824 |
| 193 and 193 | 193 |
| 100 and 23 | 2300 |