Least Common Multiple (LCM) of 27 and 128
The least common multiple (LCM) of 27 and 128 is 3456.
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 27 and 128?
First, calculate the GCD of 27 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 27 ÷ 128 = 0 remainder 27 |
| 2 | 128 ÷ 27 = 4 remainder 20 |
| 3 | 27 ÷ 20 = 1 remainder 7 |
| 4 | 20 ÷ 7 = 2 remainder 6 |
| 5 | 7 ÷ 6 = 1 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 192 | 10560 |
| 65 and 60 | 780 |
| 80 and 79 | 6320 |
| 27 and 168 | 1512 |
| 110 and 145 | 3190 |