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 |
|---|---|
| 171 and 179 | 30609 |
| 129 and 117 | 5031 |
| 121 and 72 | 8712 |
| 163 and 115 | 18745 |
| 147 and 191 | 28077 |