Least Common Multiple (LCM) of 30 and 175
The least common multiple (LCM) of 30 and 175 is 1050.
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 30 and 175?
First, calculate the GCD of 30 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 175 = 0 remainder 30 |
| 2 | 175 ÷ 30 = 5 remainder 25 |
| 3 | 30 ÷ 25 = 1 remainder 5 |
| 4 | 25 ÷ 5 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 116 | 20300 |
| 146 and 164 | 11972 |
| 15 and 134 | 2010 |
| 17 and 177 | 3009 |
| 123 and 101 | 12423 |