Least Common Multiple (LCM) of 130 and 76
The least common multiple (LCM) of 130 and 76 is 4940.
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 76?
First, calculate the GCD of 130 and 76 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 130 ÷ 76 = 1 remainder 54 |
| 2 | 76 ÷ 54 = 1 remainder 22 |
| 3 | 54 ÷ 22 = 2 remainder 10 |
| 4 | 22 ÷ 10 = 2 remainder 2 |
| 5 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 179 | 29535 |
| 77 and 49 | 539 |
| 144 and 70 | 5040 |
| 200 and 71 | 14200 |
| 40 and 31 | 1240 |