Least Common Multiple (LCM) of 75 and 102
The least common multiple (LCM) of 75 and 102 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 75 and 102?
First, calculate the GCD of 75 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 102 = 0 remainder 75 |
| 2 | 102 ÷ 75 = 1 remainder 27 |
| 3 | 75 ÷ 27 = 2 remainder 21 |
| 4 | 27 ÷ 21 = 1 remainder 6 |
| 5 | 21 ÷ 6 = 3 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 183 and 157 | 28731 |
| 84 and 165 | 4620 |
| 22 and 101 | 2222 |
| 80 and 26 | 1040 |
| 172 and 66 | 5676 |