Least Common Multiple (LCM) of 105 and 116
The least common multiple (LCM) of 105 and 116 is 12180.
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 116?
First, calculate the GCD of 105 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 116 = 0 remainder 105 |
| 2 | 116 ÷ 105 = 1 remainder 11 |
| 3 | 105 ÷ 11 = 9 remainder 6 |
| 4 | 11 ÷ 6 = 1 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 34 and 59 | 2006 |
| 28 and 167 | 4676 |
| 138 and 123 | 5658 |
| 147 and 172 | 25284 |
| 83 and 135 | 11205 |