Least Common Multiple (LCM) of 75 and 97
The least common multiple (LCM) of 75 and 97 is 7275.
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 97?
First, calculate the GCD of 75 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 97 = 0 remainder 75 |
| 2 | 97 ÷ 75 = 1 remainder 22 |
| 3 | 75 ÷ 22 = 3 remainder 9 |
| 4 | 22 ÷ 9 = 2 remainder 4 |
| 5 | 9 ÷ 4 = 2 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 193 and 22 | 4246 |
| 198 and 180 | 1980 |
| 42 and 58 | 1218 |
| 135 and 158 | 21330 |
| 83 and 49 | 4067 |