Least Common Multiple (LCM) of 114 and 127
The least common multiple (LCM) of 114 and 127 is 14478.
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 114 and 127?
First, calculate the GCD of 114 and 127 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 127 = 0 remainder 114 |
| 2 | 127 ÷ 114 = 1 remainder 13 |
| 3 | 114 ÷ 13 = 8 remainder 10 |
| 4 | 13 ÷ 10 = 1 remainder 3 |
| 5 | 10 ÷ 3 = 3 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 60 and 91 | 5460 |
| 37 and 155 | 5735 |
| 96 and 156 | 1248 |
| 141 and 50 | 7050 |
| 118 and 40 | 2360 |