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 |
|---|---|
| 75 and 48 | 1200 |
| 114 and 198 | 3762 |
| 126 and 53 | 6678 |
| 39 and 188 | 7332 |
| 184 and 175 | 32200 |