Least Common Multiple (LCM) of 175 and 67
The least common multiple (LCM) of 175 and 67 is 11725.
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 67?
First, calculate the GCD of 175 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 175 ÷ 67 = 2 remainder 41 |
| 2 | 67 ÷ 41 = 1 remainder 26 |
| 3 | 41 ÷ 26 = 1 remainder 15 |
| 4 | 26 ÷ 15 = 1 remainder 11 |
| 5 | 15 ÷ 11 = 1 remainder 4 |
| 6 | 11 ÷ 4 = 2 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 68 | 8364 |
| 71 and 122 | 8662 |
| 67 and 180 | 12060 |
| 165 and 147 | 8085 |
| 25 and 173 | 4325 |