Least Common Multiple (LCM) of 127 and 99
The least common multiple (LCM) of 127 and 99 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 127 and 99?
First, calculate the GCD of 127 and 99 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 127 ÷ 99 = 1 remainder 28 |
| 2 | 99 ÷ 28 = 3 remainder 15 |
| 3 | 28 ÷ 15 = 1 remainder 13 |
| 4 | 15 ÷ 13 = 1 remainder 2 |
| 5 | 13 ÷ 2 = 6 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 196 and 161 | 4508 |
| 195 and 11 | 2145 |
| 38 and 136 | 2584 |
| 33 and 76 | 2508 |
| 178 and 138 | 12282 |