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 |
|---|---|
| 114 and 44 | 2508 |
| 78 and 190 | 7410 |
| 150 and 111 | 5550 |
| 188 and 175 | 32900 |
| 90 and 180 | 180 |