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 |
|---|---|
| 72 and 100 | 1800 |
| 191 and 73 | 13943 |
| 104 and 82 | 4264 |
| 155 and 37 | 5735 |
| 167 and 88 | 14696 |