Least Common Multiple (LCM) of 75 and 109
The least common multiple (LCM) of 75 and 109 is 8175.
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 109?
First, calculate the GCD of 75 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 109 = 0 remainder 75 |
| 2 | 109 ÷ 75 = 1 remainder 34 |
| 3 | 75 ÷ 34 = 2 remainder 7 |
| 4 | 34 ÷ 7 = 4 remainder 6 |
| 5 | 7 ÷ 6 = 1 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 83 and 116 | 9628 |
| 126 and 86 | 5418 |
| 146 and 152 | 11096 |
| 18 and 87 | 522 |
| 75 and 102 | 2550 |