Least Common Multiple (LCM) of 177 and 107
The least common multiple (LCM) of 177 and 107 is 18939.
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 107?
First, calculate the GCD of 177 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 177 ÷ 107 = 1 remainder 70 |
| 2 | 107 ÷ 70 = 1 remainder 37 |
| 3 | 70 ÷ 37 = 1 remainder 33 |
| 4 | 37 ÷ 33 = 1 remainder 4 |
| 5 | 33 ÷ 4 = 8 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 154 and 192 | 14784 |
| 86 and 157 | 13502 |
| 159 and 195 | 10335 |
| 45 and 80 | 720 |
| 154 and 115 | 17710 |