Least Common Multiple (LCM) of 130 and 17
The least common multiple (LCM) of 130 and 17 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 130 and 17?
First, calculate the GCD of 130 and 17 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 130 ÷ 17 = 7 remainder 11 |
| 2 | 17 ÷ 11 = 1 remainder 6 |
| 3 | 11 ÷ 6 = 1 remainder 5 |
| 4 | 6 ÷ 5 = 1 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 119 and 32 | 3808 |
| 50 and 154 | 3850 |
| 11 and 182 | 2002 |
| 55 and 79 | 4345 |
| 41 and 165 | 6765 |