Least Common Multiple (LCM) of 50 and 78
The least common multiple (LCM) of 50 and 78 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 50 and 78?
First, calculate the GCD of 50 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 50 ÷ 78 = 0 remainder 50 |
| 2 | 78 ÷ 50 = 1 remainder 28 |
| 3 | 50 ÷ 28 = 1 remainder 22 |
| 4 | 28 ÷ 22 = 1 remainder 6 |
| 5 | 22 ÷ 6 = 3 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 21 | 2100 |
| 124 and 185 | 22940 |
| 50 and 79 | 3950 |
| 116 and 122 | 7076 |
| 134 and 193 | 25862 |