Least Common Multiple (LCM) of 30 and 171
The least common multiple (LCM) of 30 and 171 is 1710.
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 30 and 171?
First, calculate the GCD of 30 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 171 = 0 remainder 30 |
| 2 | 171 ÷ 30 = 5 remainder 21 |
| 3 | 30 ÷ 21 = 1 remainder 9 |
| 4 | 21 ÷ 9 = 2 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 17 | 1751 |
| 38 and 85 | 3230 |
| 104 and 74 | 3848 |
| 170 and 179 | 30430 |
| 93 and 14 | 1302 |