Least Common Multiple (LCM) of 103 and 78
The least common multiple (LCM) of 103 and 78 is 8034.
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 103 and 78?
First, calculate the GCD of 103 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 78 = 1 remainder 25 |
| 2 | 78 ÷ 25 = 3 remainder 3 |
| 3 | 25 ÷ 3 = 8 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 36 | 108 |
| 123 and 138 | 5658 |
| 142 and 36 | 2556 |
| 146 and 173 | 25258 |
| 179 and 154 | 27566 |