Least Common Multiple (LCM) of 75 and 104
The least common multiple (LCM) of 75 and 104 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 75 and 104?
First, calculate the GCD of 75 and 104 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 104 = 0 remainder 75 |
| 2 | 104 ÷ 75 = 1 remainder 29 |
| 3 | 75 ÷ 29 = 2 remainder 17 |
| 4 | 29 ÷ 17 = 1 remainder 12 |
| 5 | 17 ÷ 12 = 1 remainder 5 |
| 6 | 12 ÷ 5 = 2 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 184 and 75 | 13800 |
| 139 and 111 | 15429 |
| 124 and 154 | 9548 |
| 61 and 118 | 7198 |
| 14 and 108 | 756 |