Least Common Multiple (LCM) of 130 and 175
The least common multiple (LCM) of 130 and 175 is 4550.
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 175?
First, calculate the GCD of 130 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 130 ÷ 175 = 0 remainder 130 |
| 2 | 175 ÷ 130 = 1 remainder 45 |
| 3 | 130 ÷ 45 = 2 remainder 40 |
| 4 | 45 ÷ 40 = 1 remainder 5 |
| 5 | 40 ÷ 5 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 177 and 71 | 12567 |
| 170 and 127 | 21590 |
| 88 and 162 | 7128 |
| 160 and 73 | 11680 |
| 24 and 198 | 792 |