Least Common Multiple (LCM) of 109 and 175
The least common multiple (LCM) of 109 and 175 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 109 and 175?
First, calculate the GCD of 109 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 175 = 0 remainder 109 |
| 2 | 175 ÷ 109 = 1 remainder 66 |
| 3 | 109 ÷ 66 = 1 remainder 43 |
| 4 | 66 ÷ 43 = 1 remainder 23 |
| 5 | 43 ÷ 23 = 1 remainder 20 |
| 6 | 23 ÷ 20 = 1 remainder 3 |
| 7 | 20 ÷ 3 = 6 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 73 | 1533 |
| 108 and 200 | 5400 |
| 198 and 40 | 3960 |
| 131 and 146 | 19126 |
| 141 and 26 | 3666 |