Least Common Multiple (LCM) of 127 and 54
The least common multiple (LCM) of 127 and 54 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 127 and 54?
First, calculate the GCD of 127 and 54 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 127 ÷ 54 = 2 remainder 19 |
| 2 | 54 ÷ 19 = 2 remainder 16 |
| 3 | 19 ÷ 16 = 1 remainder 3 |
| 4 | 16 ÷ 3 = 5 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 37 and 132 | 4884 |
| 136 and 135 | 18360 |
| 132 and 142 | 9372 |
| 76 and 62 | 2356 |
| 17 and 109 | 1853 |