Least Common Multiple (LCM) of 175 and 189
The least common multiple (LCM) of 175 and 189 is 4725.
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 189?
First, calculate the GCD of 175 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 175 ÷ 189 = 0 remainder 175 |
| 2 | 189 ÷ 175 = 1 remainder 14 |
| 3 | 175 ÷ 14 = 12 remainder 7 |
| 4 | 14 ÷ 7 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 183 and 63 | 3843 |
| 40 and 145 | 1160 |
| 83 and 54 | 4482 |
| 64 and 96 | 192 |
| 97 and 164 | 15908 |