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 |
|---|---|
| 173 and 56 | 9688 |
| 31 and 184 | 5704 |
| 71 and 114 | 8094 |
| 111 and 127 | 14097 |
| 126 and 173 | 21798 |