Least Common Multiple (LCM) of 103 and 27
The least common multiple (LCM) of 103 and 27 is 2781.
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 27?
First, calculate the GCD of 103 and 27 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 27 = 3 remainder 22 |
| 2 | 27 ÷ 22 = 1 remainder 5 |
| 3 | 22 ÷ 5 = 4 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 141 | 20022 |
| 77 and 194 | 14938 |
| 161 and 181 | 29141 |
| 86 and 198 | 8514 |
| 150 and 68 | 5100 |