Least Common Multiple (LCM) of 105 and 106
The least common multiple (LCM) of 105 and 106 is 11130.
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 105 and 106?
First, calculate the GCD of 105 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 106 = 0 remainder 105 |
| 2 | 106 ÷ 105 = 1 remainder 1 |
| 3 | 105 ÷ 1 = 105 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 196 | 6272 |
| 119 and 15 | 1785 |
| 99 and 57 | 1881 |
| 80 and 72 | 720 |
| 157 and 56 | 8792 |