Least Common Multiple (LCM) of 178 and 107
The least common multiple (LCM) of 178 and 107 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 178 and 107?
First, calculate the GCD of 178 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 178 ÷ 107 = 1 remainder 71 |
| 2 | 107 ÷ 71 = 1 remainder 36 |
| 3 | 71 ÷ 36 = 1 remainder 35 |
| 4 | 36 ÷ 35 = 1 remainder 1 |
| 5 | 35 ÷ 1 = 35 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 183 | 2745 |
| 177 and 84 | 4956 |
| 153 and 144 | 2448 |
| 189 and 176 | 33264 |
| 147 and 136 | 19992 |