Least Common Multiple (LCM) of 75 and 107
The least common multiple (LCM) of 75 and 107 is 8025.
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 107?
First, calculate the GCD of 75 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 107 = 0 remainder 75 |
| 2 | 107 ÷ 75 = 1 remainder 32 |
| 3 | 75 ÷ 32 = 2 remainder 11 |
| 4 | 32 ÷ 11 = 2 remainder 10 |
| 5 | 11 ÷ 10 = 1 remainder 1 |
| 6 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 36 | 756 |
| 61 and 73 | 4453 |
| 109 and 122 | 13298 |
| 56 and 174 | 4872 |
| 10 and 60 | 60 |