Least Common Multiple (LCM) of 105 and 133
The least common multiple (LCM) of 105 and 133 is 1995.
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 133?
First, calculate the GCD of 105 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 133 = 0 remainder 105 |
| 2 | 133 ÷ 105 = 1 remainder 28 |
| 3 | 105 ÷ 28 = 3 remainder 21 |
| 4 | 28 ÷ 21 = 1 remainder 7 |
| 5 | 21 ÷ 7 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 50 | 9450 |
| 193 and 98 | 18914 |
| 119 and 154 | 2618 |
| 180 and 20 | 180 |
| 12 and 90 | 180 |