Least Common Multiple (LCM) of 75 and 177
The least common multiple (LCM) of 75 and 177 is 4425.
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 177?
First, calculate the GCD of 75 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 177 = 0 remainder 75 |
| 2 | 177 ÷ 75 = 2 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 |
|---|---|
| 81 and 133 | 10773 |
| 48 and 192 | 192 |
| 172 and 32 | 1376 |
| 157 and 192 | 30144 |
| 74 and 57 | 4218 |