Least Common Multiple (LCM) of 78 and 193
The least common multiple (LCM) of 78 and 193 is 15054.
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 193?
First, calculate the GCD of 78 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 193 = 0 remainder 78 |
| 2 | 193 ÷ 78 = 2 remainder 37 |
| 3 | 78 ÷ 37 = 2 remainder 4 |
| 4 | 37 ÷ 4 = 9 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 41 | 5904 |
| 48 and 118 | 2832 |
| 109 and 126 | 13734 |
| 14 and 178 | 1246 |
| 49 and 67 | 3283 |