Least Common Multiple (LCM) of 78 and 103
The least common multiple (LCM) of 78 and 103 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 78 and 103?
First, calculate the GCD of 78 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 103 = 0 remainder 78 |
| 2 | 103 ÷ 78 = 1 remainder 25 |
| 3 | 78 ÷ 25 = 3 remainder 3 |
| 4 | 25 ÷ 3 = 8 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 40 and 17 | 680 |
| 180 and 52 | 2340 |
| 183 and 41 | 7503 |
| 156 and 58 | 4524 |
| 21 and 134 | 2814 |