Least Common Multiple (LCM) of 45 and 104
The least common multiple (LCM) of 45 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 45 and 104?
First, calculate the GCD of 45 and 104 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 104 = 0 remainder 45 |
| 2 | 104 ÷ 45 = 2 remainder 14 |
| 3 | 45 ÷ 14 = 3 remainder 3 |
| 4 | 14 ÷ 3 = 4 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 197 | 19700 |
| 30 and 15 | 30 |
| 177 and 36 | 2124 |
| 137 and 140 | 19180 |
| 28 and 47 | 1316 |