Least Common Multiple (LCM) of 175 and 108
The least common multiple (LCM) of 175 and 108 is 18900.
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 108?
First, calculate the GCD of 175 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 175 ÷ 108 = 1 remainder 67 |
| 2 | 108 ÷ 67 = 1 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 |
|---|---|
| 67 and 85 | 5695 |
| 36 and 51 | 612 |
| 64 and 139 | 8896 |
| 87 and 81 | 2349 |
| 17 and 53 | 901 |