Least Common Multiple (LCM) of 174 and 195
The least common multiple (LCM) of 174 and 195 is 11310.
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 195?
First, calculate the GCD of 174 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 174 ÷ 195 = 0 remainder 174 |
| 2 | 195 ÷ 174 = 1 remainder 21 |
| 3 | 174 ÷ 21 = 8 remainder 6 |
| 4 | 21 ÷ 6 = 3 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 13 and 68 | 884 |
| 85 and 143 | 12155 |
| 177 and 76 | 13452 |
| 16 and 16 | 16 |
| 40 and 190 | 760 |