Least Common Multiple (LCM) of 63 and 103
The least common multiple (LCM) of 63 and 103 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 63 and 103?
First, calculate the GCD of 63 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 63 ÷ 103 = 0 remainder 63 |
| 2 | 103 ÷ 63 = 1 remainder 40 |
| 3 | 63 ÷ 40 = 1 remainder 23 |
| 4 | 40 ÷ 23 = 1 remainder 17 |
| 5 | 23 ÷ 17 = 1 remainder 6 |
| 6 | 17 ÷ 6 = 2 remainder 5 |
| 7 | 6 ÷ 5 = 1 remainder 1 |
| 8 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 178 and 63 | 11214 |
| 19 and 142 | 2698 |
| 104 and 102 | 5304 |
| 78 and 125 | 9750 |
| 185 and 77 | 14245 |