Least Common Multiple (LCM) of 108 and 175
The least common multiple (LCM) of 108 and 175 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 108 and 175?
First, calculate the GCD of 108 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 175 = 0 remainder 108 |
| 2 | 175 ÷ 108 = 1 remainder 67 |
| 3 | 108 ÷ 67 = 1 remainder 41 |
| 4 | 67 ÷ 41 = 1 remainder 26 |
| 5 | 41 ÷ 26 = 1 remainder 15 |
| 6 | 26 ÷ 15 = 1 remainder 11 |
| 7 | 15 ÷ 11 = 1 remainder 4 |
| 8 | 11 ÷ 4 = 2 remainder 3 |
| 9 | 4 ÷ 3 = 1 remainder 1 |
| 10 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 12 and 113 | 1356 |
| 87 and 22 | 1914 |
| 99 and 163 | 16137 |
| 23 and 198 | 4554 |
| 10 and 53 | 530 |