Least Common Multiple (LCM) of 128 and 143
The least common multiple (LCM) of 128 and 143 is 18304.
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 128 and 143?
First, calculate the GCD of 128 and 143 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 128 ÷ 143 = 0 remainder 128 |
| 2 | 143 ÷ 128 = 1 remainder 15 |
| 3 | 128 ÷ 15 = 8 remainder 8 |
| 4 | 15 ÷ 8 = 1 remainder 7 |
| 5 | 8 ÷ 7 = 1 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 64 and 56 | 448 |
| 120 and 165 | 1320 |
| 172 and 90 | 7740 |
| 72 and 132 | 792 |
| 130 and 20 | 260 |