Least Common Multiple (LCM) of 175 and 65
The least common multiple (LCM) of 175 and 65 is 2275.
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 175 and 65?
First, calculate the GCD of 175 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 175 ÷ 65 = 2 remainder 45 |
| 2 | 65 ÷ 45 = 1 remainder 20 |
| 3 | 45 ÷ 20 = 2 remainder 5 |
| 4 | 20 ÷ 5 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 172 and 92 | 3956 |
| 123 and 184 | 22632 |
| 116 and 140 | 4060 |
| 184 and 151 | 27784 |
| 11 and 12 | 132 |