Least Common Multiple (LCM) of 96 and 127
The least common multiple (LCM) of 96 and 127 is 12192.
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 96 and 127?
First, calculate the GCD of 96 and 127 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 96 ÷ 127 = 0 remainder 96 |
| 2 | 127 ÷ 96 = 1 remainder 31 |
| 3 | 96 ÷ 31 = 3 remainder 3 |
| 4 | 31 ÷ 3 = 10 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 47 and 14 | 658 |
| 105 and 175 | 525 |
| 172 and 40 | 1720 |
| 198 and 123 | 8118 |
| 133 and 196 | 3724 |