Least Common Multiple (LCM) of 177 and 50
The least common multiple (LCM) of 177 and 50 is 8850.
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 177 and 50?
First, calculate the GCD of 177 and 50 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 177 ÷ 50 = 3 remainder 27 |
| 2 | 50 ÷ 27 = 1 remainder 23 |
| 3 | 27 ÷ 23 = 1 remainder 4 |
| 4 | 23 ÷ 4 = 5 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 11 and 102 | 1122 |
| 162 and 133 | 21546 |
| 39 and 137 | 5343 |
| 53 and 176 | 9328 |
| 190 and 187 | 35530 |