Least Common Multiple (LCM) of 128 and 157
The least common multiple (LCM) of 128 and 157 is 20096.
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 157?
First, calculate the GCD of 128 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 128 ÷ 157 = 0 remainder 128 |
| 2 | 157 ÷ 128 = 1 remainder 29 |
| 3 | 128 ÷ 29 = 4 remainder 12 |
| 4 | 29 ÷ 12 = 2 remainder 5 |
| 5 | 12 ÷ 5 = 2 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 59 and 43 | 2537 |
| 195 and 148 | 28860 |
| 129 and 103 | 13287 |
| 60 and 45 | 180 |
| 183 and 56 | 10248 |