Least Common Multiple (LCM) of 174 and 80
The least common multiple (LCM) of 174 and 80 is 6960.
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 174 and 80?
First, calculate the GCD of 174 and 80 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 174 ÷ 80 = 2 remainder 14 |
| 2 | 80 ÷ 14 = 5 remainder 10 |
| 3 | 14 ÷ 10 = 1 remainder 4 |
| 4 | 10 ÷ 4 = 2 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 40 and 11 | 440 |
| 63 and 137 | 8631 |
| 151 and 49 | 7399 |
| 114 and 175 | 19950 |
| 186 and 171 | 10602 |