Least Common Multiple (LCM) of 17 and 58
The least common multiple (LCM) of 17 and 58 is 986.
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 58?
First, calculate the GCD of 17 and 58 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 17 ÷ 58 = 0 remainder 17 |
| 2 | 58 ÷ 17 = 3 remainder 7 |
| 3 | 17 ÷ 7 = 2 remainder 3 |
| 4 | 7 ÷ 3 = 2 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 34 and 173 | 5882 |
| 196 and 118 | 11564 |
| 141 and 14 | 1974 |
| 82 and 156 | 6396 |
| 13 and 100 | 1300 |