Least Common Multiple (LCM) of 105 and 127
The least common multiple (LCM) of 105 and 127 is 13335.
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 105 and 127?
First, calculate the GCD of 105 and 127 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 127 = 0 remainder 105 |
| 2 | 127 ÷ 105 = 1 remainder 22 |
| 3 | 105 ÷ 22 = 4 remainder 17 |
| 4 | 22 ÷ 17 = 1 remainder 5 |
| 5 | 17 ÷ 5 = 3 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 10 and 199 | 1990 |
| 96 and 21 | 672 |
| 151 and 90 | 13590 |
| 165 and 99 | 495 |
| 157 and 138 | 21666 |