Least Common Multiple (LCM) of 77 and 130
The least common multiple (LCM) of 77 and 130 is 10010.
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 77 and 130?
First, calculate the GCD of 77 and 130 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 77 ÷ 130 = 0 remainder 77 |
| 2 | 130 ÷ 77 = 1 remainder 53 |
| 3 | 77 ÷ 53 = 1 remainder 24 |
| 4 | 53 ÷ 24 = 2 remainder 5 |
| 5 | 24 ÷ 5 = 4 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 79 | 9006 |
| 32 and 144 | 288 |
| 120 and 89 | 10680 |
| 84 and 123 | 3444 |
| 197 and 61 | 12017 |