Least Common Multiple (LCM) of 34 and 194
The least common multiple (LCM) of 34 and 194 is 3298.
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 34 and 194?
First, calculate the GCD of 34 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 194 = 0 remainder 34 |
| 2 | 194 ÷ 34 = 5 remainder 24 |
| 3 | 34 ÷ 24 = 1 remainder 10 |
| 4 | 24 ÷ 10 = 2 remainder 4 |
| 5 | 10 ÷ 4 = 2 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 178 and 199 | 35422 |
| 197 and 101 | 19897 |
| 64 and 159 | 10176 |
| 39 and 169 | 507 |
| 153 and 160 | 24480 |