Least Common Multiple (LCM) of 75 and 197
The least common multiple (LCM) of 75 and 197 is 14775.
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 197?
First, calculate the GCD of 75 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 197 = 0 remainder 75 |
| 2 | 197 ÷ 75 = 2 remainder 47 |
| 3 | 75 ÷ 47 = 1 remainder 28 |
| 4 | 47 ÷ 28 = 1 remainder 19 |
| 5 | 28 ÷ 19 = 1 remainder 9 |
| 6 | 19 ÷ 9 = 2 remainder 1 |
| 7 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 20 | 620 |
| 118 and 104 | 6136 |
| 106 and 183 | 19398 |
| 178 and 33 | 5874 |
| 170 and 192 | 16320 |