Least Common Multiple (LCM) of 102 and 164
The least common multiple (LCM) of 102 and 164 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 102 and 164?
First, calculate the GCD of 102 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 164 = 0 remainder 102 |
| 2 | 164 ÷ 102 = 1 remainder 62 |
| 3 | 102 ÷ 62 = 1 remainder 40 |
| 4 | 62 ÷ 40 = 1 remainder 22 |
| 5 | 40 ÷ 22 = 1 remainder 18 |
| 6 | 22 ÷ 18 = 1 remainder 4 |
| 7 | 18 ÷ 4 = 4 remainder 2 |
| 8 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 70 and 30 | 210 |
| 120 and 36 | 360 |
| 193 and 84 | 16212 |
| 110 and 21 | 2310 |
| 135 and 178 | 24030 |