Least Common Multiple (LCM) of 71 and 116
The least common multiple (LCM) of 71 and 116 is 8236.
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 116?
First, calculate the GCD of 71 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 116 = 0 remainder 71 |
| 2 | 116 ÷ 71 = 1 remainder 45 |
| 3 | 71 ÷ 45 = 1 remainder 26 |
| 4 | 45 ÷ 26 = 1 remainder 19 |
| 5 | 26 ÷ 19 = 1 remainder 7 |
| 6 | 19 ÷ 7 = 2 remainder 5 |
| 7 | 7 ÷ 5 = 1 remainder 2 |
| 8 | 5 ÷ 2 = 2 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 16 and 77 | 1232 |
| 200 and 100 | 200 |
| 14 and 150 | 1050 |
| 40 and 165 | 1320 |
| 114 and 199 | 22686 |