Least Common Multiple (LCM) of 78 and 185
The least common multiple (LCM) of 78 and 185 is 14430.
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 185?
First, calculate the GCD of 78 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 185 = 0 remainder 78 |
| 2 | 185 ÷ 78 = 2 remainder 29 |
| 3 | 78 ÷ 29 = 2 remainder 20 |
| 4 | 29 ÷ 20 = 1 remainder 9 |
| 5 | 20 ÷ 9 = 2 remainder 2 |
| 6 | 9 ÷ 2 = 4 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 134 and 91 | 12194 |
| 40 and 112 | 560 |
| 159 and 104 | 16536 |
| 125 and 103 | 12875 |
| 82 and 24 | 984 |