Least Common Multiple (LCM) of 107 and 177
The least common multiple (LCM) of 107 and 177 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 107 and 177?
First, calculate the GCD of 107 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 177 = 0 remainder 107 |
| 2 | 177 ÷ 107 = 1 remainder 70 |
| 3 | 107 ÷ 70 = 1 remainder 37 |
| 4 | 70 ÷ 37 = 1 remainder 33 |
| 5 | 37 ÷ 33 = 1 remainder 4 |
| 6 | 33 ÷ 4 = 8 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 50 | 5150 |
| 151 and 200 | 30200 |
| 117 and 178 | 20826 |
| 102 and 165 | 5610 |
| 180 and 30 | 180 |