Least Common Multiple (LCM) of 130 and 145
The least common multiple (LCM) of 130 and 145 is 3770.
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 145?
First, calculate the GCD of 130 and 145 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 130 ÷ 145 = 0 remainder 130 |
| 2 | 145 ÷ 130 = 1 remainder 15 |
| 3 | 130 ÷ 15 = 8 remainder 10 |
| 4 | 15 ÷ 10 = 1 remainder 5 |
| 5 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 108 | 5940 |
| 13 and 132 | 1716 |
| 109 and 48 | 5232 |
| 91 and 194 | 17654 |
| 199 and 45 | 8955 |