Least Common Multiple (LCM) of 21 and 103
The least common multiple (LCM) of 21 and 103 is 2163.
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 21 and 103?
First, calculate the GCD of 21 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 103 = 0 remainder 21 |
| 2 | 103 ÷ 21 = 4 remainder 19 |
| 3 | 21 ÷ 19 = 1 remainder 2 |
| 4 | 19 ÷ 2 = 9 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 12 | 96 |
| 84 and 199 | 16716 |
| 163 and 183 | 29829 |
| 121 and 193 | 23353 |
| 42 and 29 | 1218 |