Least Common Multiple (LCM) of 106 and 175
The least common multiple (LCM) of 106 and 175 is 18550.
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 106 and 175?
First, calculate the GCD of 106 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 175 = 0 remainder 106 |
| 2 | 175 ÷ 106 = 1 remainder 69 |
| 3 | 106 ÷ 69 = 1 remainder 37 |
| 4 | 69 ÷ 37 = 1 remainder 32 |
| 5 | 37 ÷ 32 = 1 remainder 5 |
| 6 | 32 ÷ 5 = 6 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 47 and 135 | 6345 |
| 88 and 168 | 1848 |
| 87 and 10 | 870 |
| 171 and 115 | 19665 |
| 198 and 194 | 19206 |