Least Common Multiple (LCM) of 143 and 189
The least common multiple (LCM) of 143 and 189 is 27027.
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 189?
First, calculate the GCD of 143 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 143 ÷ 189 = 0 remainder 143 |
| 2 | 189 ÷ 143 = 1 remainder 46 |
| 3 | 143 ÷ 46 = 3 remainder 5 |
| 4 | 46 ÷ 5 = 9 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 63 and 21 | 63 |
| 118 and 18 | 1062 |
| 191 and 30 | 5730 |
| 164 and 148 | 6068 |
| 30 and 57 | 570 |