Least Common Multiple (LCM) of 78 and 180
The least common multiple (LCM) of 78 and 180 is 2340.
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 180?
First, calculate the GCD of 78 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 180 = 0 remainder 78 |
| 2 | 180 ÷ 78 = 2 remainder 24 |
| 3 | 78 ÷ 24 = 3 remainder 6 |
| 4 | 24 ÷ 6 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 196 and 99 | 19404 |
| 52 and 108 | 1404 |
| 130 and 199 | 25870 |
| 66 and 66 | 66 |
| 54 and 164 | 4428 |