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 |
|---|---|
| 149 and 126 | 18774 |
| 110 and 145 | 3190 |
| 25 and 189 | 4725 |
| 134 and 54 | 3618 |
| 188 and 49 | 9212 |