Least Common Multiple (LCM) of 130 and 165
The least common multiple (LCM) of 130 and 165 is 4290.
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 165?
First, calculate the GCD of 130 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 130 ÷ 165 = 0 remainder 130 |
| 2 | 165 ÷ 130 = 1 remainder 35 |
| 3 | 130 ÷ 35 = 3 remainder 25 |
| 4 | 35 ÷ 25 = 1 remainder 10 |
| 5 | 25 ÷ 10 = 2 remainder 5 |
| 6 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 18 and 73 | 1314 |
| 13 and 177 | 2301 |
| 137 and 92 | 12604 |
| 103 and 186 | 19158 |
| 25 and 56 | 1400 |