Least Common Multiple (LCM) of 78 and 50
The least common multiple (LCM) of 78 and 50 is 1950.
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 50?
First, calculate the GCD of 78 and 50 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 50 = 1 remainder 28 |
| 2 | 50 ÷ 28 = 1 remainder 22 |
| 3 | 28 ÷ 22 = 1 remainder 6 |
| 4 | 22 ÷ 6 = 3 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 103 | 3193 |
| 174 and 63 | 3654 |
| 139 and 92 | 12788 |
| 170 and 193 | 32810 |
| 184 and 94 | 8648 |