Least Common Multiple (LCM) of 128 and 159
The least common multiple (LCM) of 128 and 159 is 20352.
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 159?
First, calculate the GCD of 128 and 159 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 128 ÷ 159 = 0 remainder 128 |
| 2 | 159 ÷ 128 = 1 remainder 31 |
| 3 | 128 ÷ 31 = 4 remainder 4 |
| 4 | 31 ÷ 4 = 7 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 188 | 1316 |
| 13 and 17 | 221 |
| 46 and 109 | 5014 |
| 72 and 38 | 1368 |
| 91 and 172 | 15652 |