Least Common Multiple (LCM) of 177 and 105
The least common multiple (LCM) of 177 and 105 is 6195.
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 105?
First, calculate the GCD of 177 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 177 ÷ 105 = 1 remainder 72 |
| 2 | 105 ÷ 72 = 1 remainder 33 |
| 3 | 72 ÷ 33 = 2 remainder 6 |
| 4 | 33 ÷ 6 = 5 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 179 and 43 | 7697 |
| 174 and 109 | 18966 |
| 180 and 52 | 2340 |
| 137 and 161 | 22057 |
| 199 and 184 | 36616 |