Least Common Multiple (LCM) of 164 and 102
The least common multiple (LCM) of 164 and 102 is 8364.
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 102?
First, calculate the GCD of 164 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 164 ÷ 102 = 1 remainder 62 |
| 2 | 102 ÷ 62 = 1 remainder 40 |
| 3 | 62 ÷ 40 = 1 remainder 22 |
| 4 | 40 ÷ 22 = 1 remainder 18 |
| 5 | 22 ÷ 18 = 1 remainder 4 |
| 6 | 18 ÷ 4 = 4 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 135 | 3105 |
| 143 and 193 | 27599 |
| 194 and 133 | 25802 |
| 45 and 102 | 1530 |
| 193 and 83 | 16019 |