Least Common Multiple (LCM) of 114 and 105
The least common multiple (LCM) of 114 and 105 is 3990.
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 114 and 105?
First, calculate the GCD of 114 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 105 = 1 remainder 9 |
| 2 | 105 ÷ 9 = 11 remainder 6 |
| 3 | 9 ÷ 6 = 1 remainder 3 |
| 4 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 12 and 37 | 444 |
| 188 and 72 | 3384 |
| 122 and 100 | 6100 |
| 36 and 56 | 504 |
| 192 and 86 | 8256 |