Least Common Multiple (LCM) of 104 and 180
The least common multiple (LCM) of 104 and 180 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 104 and 180?
First, calculate the GCD of 104 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 104 ÷ 180 = 0 remainder 104 |
| 2 | 180 ÷ 104 = 1 remainder 76 |
| 3 | 104 ÷ 76 = 1 remainder 28 |
| 4 | 76 ÷ 28 = 2 remainder 20 |
| 5 | 28 ÷ 20 = 1 remainder 8 |
| 6 | 20 ÷ 8 = 2 remainder 4 |
| 7 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 82 | 8774 |
| 190 and 117 | 22230 |
| 70 and 64 | 2240 |
| 186 and 23 | 4278 |
| 160 and 129 | 20640 |