Least Common Multiple (LCM) of 67 and 175
The least common multiple (LCM) of 67 and 175 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 67 and 175?
First, calculate the GCD of 67 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 175 = 0 remainder 67 |
| 2 | 175 ÷ 67 = 2 remainder 41 |
| 3 | 67 ÷ 41 = 1 remainder 26 |
| 4 | 41 ÷ 26 = 1 remainder 15 |
| 5 | 26 ÷ 15 = 1 remainder 11 |
| 6 | 15 ÷ 11 = 1 remainder 4 |
| 7 | 11 ÷ 4 = 2 remainder 3 |
| 8 | 4 ÷ 3 = 1 remainder 1 |
| 9 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 178 and 63 | 11214 |
| 45 and 200 | 1800 |
| 112 and 165 | 18480 |
| 112 and 168 | 336 |
| 165 and 103 | 16995 |