Least Common Multiple (LCM) of 102 and 75
The least common multiple (LCM) of 102 and 75 is 2550.
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 102 and 75?
First, calculate the GCD of 102 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 75 = 1 remainder 27 |
| 2 | 75 ÷ 27 = 2 remainder 21 |
| 3 | 27 ÷ 21 = 1 remainder 6 |
| 4 | 21 ÷ 6 = 3 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 96 | 1440 |
| 14 and 142 | 994 |
| 157 and 82 | 12874 |
| 15 and 184 | 2760 |
| 188 and 40 | 1880 |