Least Common Multiple (LCM) of 121 and 105
The least common multiple (LCM) of 121 and 105 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 121 and 105?
First, calculate the GCD of 121 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 121 ÷ 105 = 1 remainder 16 |
| 2 | 105 ÷ 16 = 6 remainder 9 |
| 3 | 16 ÷ 9 = 1 remainder 7 |
| 4 | 9 ÷ 7 = 1 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 36 | 180 |
| 172 and 30 | 2580 |
| 143 and 114 | 16302 |
| 95 and 31 | 2945 |
| 37 and 66 | 2442 |