Least Common Multiple (LCM) of 106 and 75
The least common multiple (LCM) of 106 and 75 is 7950.
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 75?
First, calculate the GCD of 106 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 75 = 1 remainder 31 |
| 2 | 75 ÷ 31 = 2 remainder 13 |
| 3 | 31 ÷ 13 = 2 remainder 5 |
| 4 | 13 ÷ 5 = 2 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 182 and 18 | 1638 |
| 45 and 110 | 990 |
| 177 and 167 | 29559 |
| 30 and 30 | 30 |
| 30 and 77 | 2310 |