Least Common Multiple (LCM) of 103 and 121
The least common multiple (LCM) of 103 and 121 is 12463.
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 121?
First, calculate the GCD of 103 and 121 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 121 = 0 remainder 103 |
| 2 | 121 ÷ 103 = 1 remainder 18 |
| 3 | 103 ÷ 18 = 5 remainder 13 |
| 4 | 18 ÷ 13 = 1 remainder 5 |
| 5 | 13 ÷ 5 = 2 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 178 and 16 | 1424 |
| 104 and 30 | 1560 |
| 168 and 189 | 1512 |
| 70 and 51 | 3570 |
| 182 and 171 | 31122 |