Least Common Multiple (LCM) of 130 and 178
The least common multiple (LCM) of 130 and 178 is 11570.
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 178?
First, calculate the GCD of 130 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 130 ÷ 178 = 0 remainder 130 |
| 2 | 178 ÷ 130 = 1 remainder 48 |
| 3 | 130 ÷ 48 = 2 remainder 34 |
| 4 | 48 ÷ 34 = 1 remainder 14 |
| 5 | 34 ÷ 14 = 2 remainder 6 |
| 6 | 14 ÷ 6 = 2 remainder 2 |
| 7 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 75 and 99 | 2475 |
| 75 and 167 | 12525 |
| 180 and 82 | 7380 |
| 17 and 145 | 2465 |
| 158 and 44 | 3476 |