Least Common Multiple (LCM) of 99 and 127
The least common multiple (LCM) of 99 and 127 is 12573.
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 99 and 127?
First, calculate the GCD of 99 and 127 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 127 = 0 remainder 99 |
| 2 | 127 ÷ 99 = 1 remainder 28 |
| 3 | 99 ÷ 28 = 3 remainder 15 |
| 4 | 28 ÷ 15 = 1 remainder 13 |
| 5 | 15 ÷ 13 = 1 remainder 2 |
| 6 | 13 ÷ 2 = 6 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 119 and 188 | 22372 |
| 195 and 89 | 17355 |
| 43 and 191 | 8213 |
| 133 and 108 | 14364 |
| 35 and 172 | 6020 |