Least Common Multiple (LCM) of 175 and 106
The least common multiple (LCM) of 175 and 106 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 175 and 106?
First, calculate the GCD of 175 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 175 ÷ 106 = 1 remainder 69 |
| 2 | 106 ÷ 69 = 1 remainder 37 |
| 3 | 69 ÷ 37 = 1 remainder 32 |
| 4 | 37 ÷ 32 = 1 remainder 5 |
| 5 | 32 ÷ 5 = 6 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 42 | 336 |
| 170 and 166 | 14110 |
| 133 and 71 | 9443 |
| 75 and 152 | 11400 |
| 186 and 97 | 18042 |