Least Common Multiple (LCM) of 174 and 194
The least common multiple (LCM) of 174 and 194 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 174 and 194?
First, calculate the GCD of 174 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 174 ÷ 194 = 0 remainder 174 |
| 2 | 194 ÷ 174 = 1 remainder 20 |
| 3 | 174 ÷ 20 = 8 remainder 14 |
| 4 | 20 ÷ 14 = 1 remainder 6 |
| 5 | 14 ÷ 6 = 2 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 94 | 5076 |
| 17 and 98 | 1666 |
| 48 and 96 | 96 |
| 149 and 113 | 16837 |
| 72 and 151 | 10872 |