Least Common Multiple (LCM) of 128 and 177
The least common multiple (LCM) of 128 and 177 is 22656.
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 177?
First, calculate the GCD of 128 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 128 ÷ 177 = 0 remainder 128 |
| 2 | 177 ÷ 128 = 1 remainder 49 |
| 3 | 128 ÷ 49 = 2 remainder 30 |
| 4 | 49 ÷ 30 = 1 remainder 19 |
| 5 | 30 ÷ 19 = 1 remainder 11 |
| 6 | 19 ÷ 11 = 1 remainder 8 |
| 7 | 11 ÷ 8 = 1 remainder 3 |
| 8 | 8 ÷ 3 = 2 remainder 2 |
| 9 | 3 ÷ 2 = 1 remainder 1 |
| 10 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 178 and 191 | 33998 |
| 14 and 30 | 210 |
| 86 and 197 | 16942 |
| 34 and 151 | 5134 |
| 186 and 93 | 186 |