Least Common Multiple (LCM) of 102 and 171
The least common multiple (LCM) of 102 and 171 is 5814.
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 171?
First, calculate the GCD of 102 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 171 = 0 remainder 102 |
| 2 | 171 ÷ 102 = 1 remainder 69 |
| 3 | 102 ÷ 69 = 1 remainder 33 |
| 4 | 69 ÷ 33 = 2 remainder 3 |
| 5 | 33 ÷ 3 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 47 and 141 | 141 |
| 47 and 81 | 3807 |
| 80 and 78 | 3120 |
| 138 and 116 | 8004 |
| 70 and 71 | 4970 |