Least Common Multiple (LCM) of 71 and 123
The least common multiple (LCM) of 71 and 123 is 8733.
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 123?
First, calculate the GCD of 71 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 123 = 0 remainder 71 |
| 2 | 123 ÷ 71 = 1 remainder 52 |
| 3 | 71 ÷ 52 = 1 remainder 19 |
| 4 | 52 ÷ 19 = 2 remainder 14 |
| 5 | 19 ÷ 14 = 1 remainder 5 |
| 6 | 14 ÷ 5 = 2 remainder 4 |
| 7 | 5 ÷ 4 = 1 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 69 | 4416 |
| 126 and 76 | 4788 |
| 32 and 45 | 1440 |
| 12 and 41 | 492 |
| 40 and 197 | 7880 |