Least Common Multiple (LCM) of 102 and 178
The least common multiple (LCM) of 102 and 178 is 9078.
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 102 and 178?
First, calculate the GCD of 102 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 178 = 0 remainder 102 |
| 2 | 178 ÷ 102 = 1 remainder 76 |
| 3 | 102 ÷ 76 = 1 remainder 26 |
| 4 | 76 ÷ 26 = 2 remainder 24 |
| 5 | 26 ÷ 24 = 1 remainder 2 |
| 6 | 24 ÷ 2 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 116 and 194 | 11252 |
| 188 and 135 | 25380 |
| 165 and 89 | 14685 |
| 148 and 180 | 6660 |
| 182 and 168 | 2184 |