Least Common Multiple (LCM) of 107 and 178
The least common multiple (LCM) of 107 and 178 is 19046.
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 178?
First, calculate the GCD of 107 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 178 = 0 remainder 107 |
| 2 | 178 ÷ 107 = 1 remainder 71 |
| 3 | 107 ÷ 71 = 1 remainder 36 |
| 4 | 71 ÷ 36 = 1 remainder 35 |
| 5 | 36 ÷ 35 = 1 remainder 1 |
| 6 | 35 ÷ 1 = 35 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 77 and 166 | 12782 |
| 114 and 19 | 114 |
| 181 and 104 | 18824 |
| 158 and 66 | 5214 |
| 117 and 109 | 12753 |