Least Common Multiple (LCM) of 164 and 129
The least common multiple (LCM) of 164 and 129 is 21156.
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 129?
First, calculate the GCD of 164 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 164 ÷ 129 = 1 remainder 35 |
| 2 | 129 ÷ 35 = 3 remainder 24 |
| 3 | 35 ÷ 24 = 1 remainder 11 |
| 4 | 24 ÷ 11 = 2 remainder 2 |
| 5 | 11 ÷ 2 = 5 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 44 and 86 | 1892 |
| 20 and 44 | 220 |
| 175 and 107 | 18725 |
| 168 and 198 | 5544 |
| 112 and 111 | 12432 |