Least Common Multiple (LCM) of 74 and 176
The least common multiple (LCM) of 74 and 176 is 6512.
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 176?
First, calculate the GCD of 74 and 176 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 74 ÷ 176 = 0 remainder 74 |
| 2 | 176 ÷ 74 = 2 remainder 28 |
| 3 | 74 ÷ 28 = 2 remainder 18 |
| 4 | 28 ÷ 18 = 1 remainder 10 |
| 5 | 18 ÷ 10 = 1 remainder 8 |
| 6 | 10 ÷ 8 = 1 remainder 2 |
| 7 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 187 and 110 | 1870 |
| 82 and 24 | 984 |
| 137 and 162 | 22194 |
| 113 and 131 | 14803 |
| 18 and 56 | 504 |