Least Common Multiple (LCM) of 194 and 174
The least common multiple (LCM) of 194 and 174 is 16878.
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 194 and 174?
First, calculate the GCD of 194 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 194 ÷ 174 = 1 remainder 20 |
| 2 | 174 ÷ 20 = 8 remainder 14 |
| 3 | 20 ÷ 14 = 1 remainder 6 |
| 4 | 14 ÷ 6 = 2 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 100 | 5300 |
| 159 and 53 | 159 |
| 49 and 156 | 7644 |
| 73 and 186 | 13578 |
| 138 and 82 | 5658 |