Least Common Multiple (LCM) of 71 and 103
The least common multiple (LCM) of 71 and 103 is 7313.
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 103?
First, calculate the GCD of 71 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 103 = 0 remainder 71 |
| 2 | 103 ÷ 71 = 1 remainder 32 |
| 3 | 71 ÷ 32 = 2 remainder 7 |
| 4 | 32 ÷ 7 = 4 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 104 | 2808 |
| 118 and 22 | 1298 |
| 83 and 165 | 13695 |
| 149 and 120 | 17880 |
| 31 and 139 | 4309 |