Least Common Multiple (LCM) of 74 and 178
The least common multiple (LCM) of 74 and 178 is 6586.
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 74 and 178?
First, calculate the GCD of 74 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 74 ÷ 178 = 0 remainder 74 |
| 2 | 178 ÷ 74 = 2 remainder 30 |
| 3 | 74 ÷ 30 = 2 remainder 14 |
| 4 | 30 ÷ 14 = 2 remainder 2 |
| 5 | 14 ÷ 2 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 75 and 179 | 13425 |
| 162 and 170 | 13770 |
| 127 and 33 | 4191 |
| 131 and 67 | 8777 |
| 86 and 148 | 6364 |