Least Common Multiple (LCM) of 117 and 105
The least common multiple (LCM) of 117 and 105 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 117 and 105?
First, calculate the GCD of 117 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 105 = 1 remainder 12 |
| 2 | 105 ÷ 12 = 8 remainder 9 |
| 3 | 12 ÷ 9 = 1 remainder 3 |
| 4 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 24 and 96 | 96 |
| 159 and 101 | 16059 |
| 20 and 195 | 780 |
| 32 and 123 | 3936 |
| 114 and 30 | 570 |