Least Common Multiple (LCM) of 78 and 184
The least common multiple (LCM) of 78 and 184 is 7176.
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 184?
First, calculate the GCD of 78 and 184 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 184 = 0 remainder 78 |
| 2 | 184 ÷ 78 = 2 remainder 28 |
| 3 | 78 ÷ 28 = 2 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 |
|---|---|
| 145 and 70 | 2030 |
| 104 and 76 | 1976 |
| 183 and 172 | 31476 |
| 107 and 80 | 8560 |
| 91 and 133 | 1729 |