Least Common Multiple (LCM) of 75 and 191
The least common multiple (LCM) of 75 and 191 is 14325.
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 191?
First, calculate the GCD of 75 and 191 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 191 = 0 remainder 75 |
| 2 | 191 ÷ 75 = 2 remainder 41 |
| 3 | 75 ÷ 41 = 1 remainder 34 |
| 4 | 41 ÷ 34 = 1 remainder 7 |
| 5 | 34 ÷ 7 = 4 remainder 6 |
| 6 | 7 ÷ 6 = 1 remainder 1 |
| 7 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 118 and 36 | 2124 |
| 182 and 82 | 7462 |
| 90 and 179 | 16110 |
| 178 and 99 | 17622 |
| 51 and 112 | 5712 |