Least Common Multiple (LCM) of 102 and 159
The least common multiple (LCM) of 102 and 159 is 5406.
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 159?
First, calculate the GCD of 102 and 159 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 159 = 0 remainder 102 |
| 2 | 159 ÷ 102 = 1 remainder 57 |
| 3 | 102 ÷ 57 = 1 remainder 45 |
| 4 | 57 ÷ 45 = 1 remainder 12 |
| 5 | 45 ÷ 12 = 3 remainder 9 |
| 6 | 12 ÷ 9 = 1 remainder 3 |
| 7 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 194 | 6014 |
| 194 and 99 | 19206 |
| 184 and 75 | 13800 |
| 200 and 118 | 11800 |
| 45 and 135 | 135 |