Least Common Multiple (LCM) of 103 and 63
The least common multiple (LCM) of 103 and 63 is 6489.
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 63?
First, calculate the GCD of 103 and 63 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 63 = 1 remainder 40 |
| 2 | 63 ÷ 40 = 1 remainder 23 |
| 3 | 40 ÷ 23 = 1 remainder 17 |
| 4 | 23 ÷ 17 = 1 remainder 6 |
| 5 | 17 ÷ 6 = 2 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 86 and 104 | 4472 |
| 185 and 166 | 30710 |
| 75 and 43 | 3225 |
| 150 and 132 | 3300 |
| 47 and 90 | 4230 |