Least Common Multiple (LCM) of 175 and 109
The least common multiple (LCM) of 175 and 109 is 19075.
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 109?
First, calculate the GCD of 175 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 175 ÷ 109 = 1 remainder 66 |
| 2 | 109 ÷ 66 = 1 remainder 43 |
| 3 | 66 ÷ 43 = 1 remainder 23 |
| 4 | 43 ÷ 23 = 1 remainder 20 |
| 5 | 23 ÷ 20 = 1 remainder 3 |
| 6 | 20 ÷ 3 = 6 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 176 and 15 | 2640 |
| 194 and 145 | 28130 |
| 180 and 62 | 5580 |
| 198 and 133 | 26334 |
| 187 and 109 | 20383 |