Least Common Multiple (LCM) of 83 and 75
The least common multiple (LCM) of 83 and 75 is 6225.
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 83 and 75?
First, calculate the GCD of 83 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 75 = 1 remainder 8 |
| 2 | 75 ÷ 8 = 9 remainder 3 |
| 3 | 8 ÷ 3 = 2 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 170 and 93 | 15810 |
| 130 and 73 | 9490 |
| 84 and 140 | 420 |
| 112 and 125 | 14000 |
| 126 and 195 | 8190 |