Least Common Multiple (LCM) of 71 and 115
The least common multiple (LCM) of 71 and 115 is 8165.
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 115?
First, calculate the GCD of 71 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 115 = 0 remainder 71 |
| 2 | 115 ÷ 71 = 1 remainder 44 |
| 3 | 71 ÷ 44 = 1 remainder 27 |
| 4 | 44 ÷ 27 = 1 remainder 17 |
| 5 | 27 ÷ 17 = 1 remainder 10 |
| 6 | 17 ÷ 10 = 1 remainder 7 |
| 7 | 10 ÷ 7 = 1 remainder 3 |
| 8 | 7 ÷ 3 = 2 remainder 1 |
| 9 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 185 and 117 | 21645 |
| 32 and 131 | 4192 |
| 31 and 135 | 4185 |
| 40 and 145 | 1160 |
| 97 and 80 | 7760 |