Least Common Multiple (LCM) of 104 and 178
The least common multiple (LCM) of 104 and 178 is 9256.
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 104 and 178?
First, calculate the GCD of 104 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 104 ÷ 178 = 0 remainder 104 |
| 2 | 178 ÷ 104 = 1 remainder 74 |
| 3 | 104 ÷ 74 = 1 remainder 30 |
| 4 | 74 ÷ 30 = 2 remainder 14 |
| 5 | 30 ÷ 14 = 2 remainder 2 |
| 6 | 14 ÷ 2 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 123 | 15990 |
| 80 and 85 | 1360 |
| 156 and 185 | 28860 |
| 51 and 80 | 4080 |
| 166 and 42 | 3486 |