Least Common Multiple (LCM) of 78 and 127
The least common multiple (LCM) of 78 and 127 is 9906.
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 78 and 127?
First, calculate the GCD of 78 and 127 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 127 = 0 remainder 78 |
| 2 | 127 ÷ 78 = 1 remainder 49 |
| 3 | 78 ÷ 49 = 1 remainder 29 |
| 4 | 49 ÷ 29 = 1 remainder 20 |
| 5 | 29 ÷ 20 = 1 remainder 9 |
| 6 | 20 ÷ 9 = 2 remainder 2 |
| 7 | 9 ÷ 2 = 4 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 34 and 96 | 1632 |
| 165 and 39 | 2145 |
| 199 and 87 | 17313 |
| 106 and 179 | 18974 |
| 136 and 197 | 26792 |