Least Common Multiple (LCM) of 46 and 171
The least common multiple (LCM) of 46 and 171 is 7866.
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 46 and 171?
First, calculate the GCD of 46 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 46 ÷ 171 = 0 remainder 46 |
| 2 | 171 ÷ 46 = 3 remainder 33 |
| 3 | 46 ÷ 33 = 1 remainder 13 |
| 4 | 33 ÷ 13 = 2 remainder 7 |
| 5 | 13 ÷ 7 = 1 remainder 6 |
| 6 | 7 ÷ 6 = 1 remainder 1 |
| 7 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 83 and 184 | 15272 |
| 123 and 24 | 984 |
| 106 and 21 | 2226 |
| 135 and 171 | 2565 |
| 165 and 74 | 12210 |