Least Common Multiple (LCM) of 130 and 149
The least common multiple (LCM) of 130 and 149 is 19370.
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 149?
First, calculate the GCD of 130 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 130 ÷ 149 = 0 remainder 130 |
| 2 | 149 ÷ 130 = 1 remainder 19 |
| 3 | 130 ÷ 19 = 6 remainder 16 |
| 4 | 19 ÷ 16 = 1 remainder 3 |
| 5 | 16 ÷ 3 = 5 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 41 and 70 | 2870 |
| 96 and 165 | 5280 |
| 64 and 109 | 6976 |
| 29 and 187 | 5423 |
| 52 and 130 | 260 |