Least Common Multiple (LCM) of 133 and 164
The least common multiple (LCM) of 133 and 164 is 21812.
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 133 and 164?
First, calculate the GCD of 133 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 133 ÷ 164 = 0 remainder 133 |
| 2 | 164 ÷ 133 = 1 remainder 31 |
| 3 | 133 ÷ 31 = 4 remainder 9 |
| 4 | 31 ÷ 9 = 3 remainder 4 |
| 5 | 9 ÷ 4 = 2 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 81 | 2835 |
| 181 and 88 | 15928 |
| 134 and 143 | 19162 |
| 118 and 105 | 12390 |
| 31 and 77 | 2387 |