Least Common Multiple (LCM) of 27 and 127
The least common multiple (LCM) of 27 and 127 is 3429.
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 127?
First, calculate the GCD of 27 and 127 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 27 ÷ 127 = 0 remainder 27 |
| 2 | 127 ÷ 27 = 4 remainder 19 |
| 3 | 27 ÷ 19 = 1 remainder 8 |
| 4 | 19 ÷ 8 = 2 remainder 3 |
| 5 | 8 ÷ 3 = 2 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 118 and 39 | 4602 |
| 189 and 177 | 11151 |
| 129 and 64 | 8256 |
| 41 and 12 | 492 |
| 101 and 65 | 6565 |