Least Common Multiple (LCM) of 180 and 78
The least common multiple (LCM) of 180 and 78 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 180 and 78?
First, calculate the GCD of 180 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 78 = 2 remainder 24 |
| 2 | 78 ÷ 24 = 3 remainder 6 |
| 3 | 24 ÷ 6 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 99 and 145 | 14355 |
| 95 and 96 | 9120 |
| 120 and 99 | 3960 |
| 155 and 28 | 4340 |
| 20 and 56 | 280 |