Least Common Multiple (LCM) of 180 and 104
The least common multiple (LCM) of 180 and 104 is 4680.
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 104?
First, calculate the GCD of 180 and 104 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 104 = 1 remainder 76 |
| 2 | 104 ÷ 76 = 1 remainder 28 |
| 3 | 76 ÷ 28 = 2 remainder 20 |
| 4 | 28 ÷ 20 = 1 remainder 8 |
| 5 | 20 ÷ 8 = 2 remainder 4 |
| 6 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 24 | 408 |
| 20 and 11 | 220 |
| 24 and 194 | 2328 |
| 173 and 48 | 8304 |
| 16 and 23 | 368 |