Least Common Multiple (LCM) of 174 and 196
The least common multiple (LCM) of 174 and 196 is 17052.
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 196?
First, calculate the GCD of 174 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 174 ÷ 196 = 0 remainder 174 |
| 2 | 196 ÷ 174 = 1 remainder 22 |
| 3 | 174 ÷ 22 = 7 remainder 20 |
| 4 | 22 ÷ 20 = 1 remainder 2 |
| 5 | 20 ÷ 2 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 199 and 171 | 34029 |
| 70 and 56 | 280 |
| 65 and 40 | 520 |
| 18 and 17 | 306 |
| 102 and 76 | 3876 |