Least Common Multiple (LCM) of 105 and 121
The least common multiple (LCM) of 105 and 121 is 12705.
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 105 and 121?
First, calculate the GCD of 105 and 121 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 121 = 0 remainder 105 |
| 2 | 121 ÷ 105 = 1 remainder 16 |
| 3 | 105 ÷ 16 = 6 remainder 9 |
| 4 | 16 ÷ 9 = 1 remainder 7 |
| 5 | 9 ÷ 7 = 1 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 51 and 117 | 1989 |
| 194 and 82 | 7954 |
| 148 and 148 | 148 |
| 38 and 38 | 38 |
| 23 and 123 | 2829 |