Least Common Multiple (LCM) of 164 and 133
The least common multiple (LCM) of 164 and 133 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 164 and 133?
First, calculate the GCD of 164 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 164 ÷ 133 = 1 remainder 31 |
| 2 | 133 ÷ 31 = 4 remainder 9 |
| 3 | 31 ÷ 9 = 3 remainder 4 |
| 4 | 9 ÷ 4 = 2 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 100 | 3200 |
| 70 and 145 | 2030 |
| 177 and 23 | 4071 |
| 171 and 102 | 5814 |
| 157 and 174 | 27318 |