Least Common Multiple (LCM) of 102 and 163
The least common multiple (LCM) of 102 and 163 is 16626.
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 163?
First, calculate the GCD of 102 and 163 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 163 = 0 remainder 102 |
| 2 | 163 ÷ 102 = 1 remainder 61 |
| 3 | 102 ÷ 61 = 1 remainder 41 |
| 4 | 61 ÷ 41 = 1 remainder 20 |
| 5 | 41 ÷ 20 = 2 remainder 1 |
| 6 | 20 ÷ 1 = 20 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 19 and 107 | 2033 |
| 70 and 73 | 5110 |
| 37 and 46 | 1702 |
| 72 and 80 | 720 |
| 45 and 20 | 180 |