Least Common Multiple (LCM) of 17 and 130
The least common multiple (LCM) of 17 and 130 is 2210.
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 130?
First, calculate the GCD of 17 and 130 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 17 ÷ 130 = 0 remainder 17 |
| 2 | 130 ÷ 17 = 7 remainder 11 |
| 3 | 17 ÷ 11 = 1 remainder 6 |
| 4 | 11 ÷ 6 = 1 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 145 | 2320 |
| 186 and 40 | 3720 |
| 59 and 48 | 2832 |
| 183 and 91 | 16653 |
| 190 and 85 | 3230 |