Least Common Multiple (LCM) of 123 and 71
The least common multiple (LCM) of 123 and 71 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 123 and 71?
First, calculate the GCD of 123 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 71 = 1 remainder 52 |
| 2 | 71 ÷ 52 = 1 remainder 19 |
| 3 | 52 ÷ 19 = 2 remainder 14 |
| 4 | 19 ÷ 14 = 1 remainder 5 |
| 5 | 14 ÷ 5 = 2 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 127 and 176 | 22352 |
| 100 and 80 | 400 |
| 83 and 75 | 6225 |
| 193 and 77 | 14861 |
| 193 and 154 | 29722 |