Least Common Multiple (LCM) of 17 and 134
The least common multiple (LCM) of 17 and 134 is 2278.
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 17 and 134?
First, calculate the GCD of 17 and 134 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 17 ÷ 134 = 0 remainder 17 |
| 2 | 134 ÷ 17 = 7 remainder 15 |
| 3 | 17 ÷ 15 = 1 remainder 2 |
| 4 | 15 ÷ 2 = 7 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 33 and 41 | 1353 |
| 135 and 49 | 6615 |
| 99 and 20 | 1980 |
| 167 and 82 | 13694 |
| 183 and 176 | 32208 |