Least Common Multiple (LCM) of 121 and 107
The least common multiple (LCM) of 121 and 107 is 12947.
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 107?
First, calculate the GCD of 121 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 121 ÷ 107 = 1 remainder 14 |
| 2 | 107 ÷ 14 = 7 remainder 9 |
| 3 | 14 ÷ 9 = 1 remainder 5 |
| 4 | 9 ÷ 5 = 1 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 131 and 138 | 18078 |
| 70 and 190 | 1330 |
| 145 and 116 | 580 |
| 183 and 162 | 9882 |
| 125 and 68 | 8500 |