Least Common Multiple (LCM) of 104 and 75
The least common multiple (LCM) of 104 and 75 is 7800.
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 75?
First, calculate the GCD of 104 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 104 ÷ 75 = 1 remainder 29 |
| 2 | 75 ÷ 29 = 2 remainder 17 |
| 3 | 29 ÷ 17 = 1 remainder 12 |
| 4 | 17 ÷ 12 = 1 remainder 5 |
| 5 | 12 ÷ 5 = 2 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 194 and 131 | 25414 |
| 46 and 61 | 2806 |
| 168 and 77 | 1848 |
| 182 and 74 | 6734 |
| 190 and 178 | 16910 |