Least Common Multiple (LCM) of 104 and 45
The least common multiple (LCM) of 104 and 45 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 45?
First, calculate the GCD of 104 and 45 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 104 ÷ 45 = 2 remainder 14 |
| 2 | 45 ÷ 14 = 3 remainder 3 |
| 3 | 14 ÷ 3 = 4 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 104 and 37 | 3848 |
| 171 and 45 | 855 |
| 174 and 77 | 13398 |
| 134 and 26 | 1742 |
| 79 and 59 | 4661 |