Least Common Multiple (LCM) of 130 and 177
The least common multiple (LCM) of 130 and 177 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 130 and 177?
First, calculate the GCD of 130 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 130 ÷ 177 = 0 remainder 130 |
| 2 | 177 ÷ 130 = 1 remainder 47 |
| 3 | 130 ÷ 47 = 2 remainder 36 |
| 4 | 47 ÷ 36 = 1 remainder 11 |
| 5 | 36 ÷ 11 = 3 remainder 3 |
| 6 | 11 ÷ 3 = 3 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 193 and 191 | 36863 |
| 109 and 185 | 20165 |
| 140 and 102 | 7140 |
| 110 and 141 | 15510 |
| 112 and 61 | 6832 |