Least Common Multiple (LCM) of 71 and 168
The least common multiple (LCM) of 71 and 168 is 11928.
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 71 and 168?
First, calculate the GCD of 71 and 168 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 168 = 0 remainder 71 |
| 2 | 168 ÷ 71 = 2 remainder 26 |
| 3 | 71 ÷ 26 = 2 remainder 19 |
| 4 | 26 ÷ 19 = 1 remainder 7 |
| 5 | 19 ÷ 7 = 2 remainder 5 |
| 6 | 7 ÷ 5 = 1 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 49 and 46 | 2254 |
| 18 and 192 | 576 |
| 41 and 164 | 164 |
| 169 and 105 | 17745 |
| 31 and 118 | 3658 |