Least Common Multiple (LCM) of 54 and 127
The least common multiple (LCM) of 54 and 127 is 6858.
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 54 and 127?
First, calculate the GCD of 54 and 127 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 127 = 0 remainder 54 |
| 2 | 127 ÷ 54 = 2 remainder 19 |
| 3 | 54 ÷ 19 = 2 remainder 16 |
| 4 | 19 ÷ 16 = 1 remainder 3 |
| 5 | 16 ÷ 3 = 5 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 155 | 3100 |
| 165 and 91 | 15015 |
| 34 and 101 | 3434 |
| 43 and 20 | 860 |
| 136 and 16 | 272 |