Least Common Multiple (LCM) of 159 and 102
The least common multiple (LCM) of 159 and 102 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 159 and 102?
First, calculate the GCD of 159 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 159 ÷ 102 = 1 remainder 57 |
| 2 | 102 ÷ 57 = 1 remainder 45 |
| 3 | 57 ÷ 45 = 1 remainder 12 |
| 4 | 45 ÷ 12 = 3 remainder 9 |
| 5 | 12 ÷ 9 = 1 remainder 3 |
| 6 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 46 and 31 | 1426 |
| 92 and 104 | 2392 |
| 120 and 191 | 22920 |
| 117 and 82 | 9594 |
| 198 and 78 | 2574 |