Least Common Multiple (LCM) of 123 and 143
The least common multiple (LCM) of 123 and 143 is 17589.
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 123 and 143?
First, calculate the GCD of 123 and 143 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 143 = 0 remainder 123 |
| 2 | 143 ÷ 123 = 1 remainder 20 |
| 3 | 123 ÷ 20 = 6 remainder 3 |
| 4 | 20 ÷ 3 = 6 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 186 | 10416 |
| 163 and 21 | 3423 |
| 140 and 148 | 5180 |
| 89 and 79 | 7031 |
| 104 and 58 | 3016 |