Least Common Multiple (LCM) of 19 and 175
The least common multiple (LCM) of 19 and 175 is 3325.
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 19 and 175?
First, calculate the GCD of 19 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 19 ÷ 175 = 0 remainder 19 |
| 2 | 175 ÷ 19 = 9 remainder 4 |
| 3 | 19 ÷ 4 = 4 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 20 | 420 |
| 30 and 198 | 990 |
| 153 and 22 | 3366 |
| 170 and 105 | 3570 |
| 69 and 68 | 4692 |