Least Common Multiple (LCM) of 177 and 130
The least common multiple (LCM) of 177 and 130 is 23010.
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 177 and 130?
First, calculate the GCD of 177 and 130 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 177 ÷ 130 = 1 remainder 47 |
| 2 | 130 ÷ 47 = 2 remainder 36 |
| 3 | 47 ÷ 36 = 1 remainder 11 |
| 4 | 36 ÷ 11 = 3 remainder 3 |
| 5 | 11 ÷ 3 = 3 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 24 and 177 | 1416 |
| 67 and 193 | 12931 |
| 160 and 67 | 10720 |
| 110 and 145 | 3190 |
| 198 and 43 | 8514 |