Least Common Multiple (LCM) of 105 and 117
The least common multiple (LCM) of 105 and 117 is 4095.
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 117?
First, calculate the GCD of 105 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 117 = 0 remainder 105 |
| 2 | 117 ÷ 105 = 1 remainder 12 |
| 3 | 105 ÷ 12 = 8 remainder 9 |
| 4 | 12 ÷ 9 = 1 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 111 and 90 | 3330 |
| 192 and 75 | 4800 |
| 76 and 83 | 6308 |
| 57 and 105 | 1995 |
| 128 and 122 | 7808 |