Least Common Multiple (LCM) of 103 and 71
The least common multiple (LCM) of 103 and 71 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 103 and 71?
First, calculate the GCD of 103 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 71 = 1 remainder 32 |
| 2 | 71 ÷ 32 = 2 remainder 7 |
| 3 | 32 ÷ 7 = 4 remainder 4 |
| 4 | 7 ÷ 4 = 1 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 163 and 54 | 8802 |
| 87 and 137 | 11919 |
| 33 and 30 | 330 |
| 82 and 102 | 4182 |
| 170 and 134 | 11390 |