Least Common Multiple (LCM) of 116 and 75
The least common multiple (LCM) of 116 and 75 is 8700.
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 116 and 75?
First, calculate the GCD of 116 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 75 = 1 remainder 41 |
| 2 | 75 ÷ 41 = 1 remainder 34 |
| 3 | 41 ÷ 34 = 1 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 |
|---|---|
| 105 and 131 | 13755 |
| 150 and 51 | 2550 |
| 84 and 186 | 2604 |
| 92 and 128 | 2944 |
| 16 and 200 | 400 |