Least Common Multiple (LCM) of 116 and 103
The least common multiple (LCM) of 116 and 103 is 11948.
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 116 and 103?
First, calculate the GCD of 116 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 103 = 1 remainder 13 |
| 2 | 103 ÷ 13 = 7 remainder 12 |
| 3 | 13 ÷ 12 = 1 remainder 1 |
| 4 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 127 and 127 | 127 |
| 96 and 165 | 5280 |
| 175 and 67 | 11725 |
| 166 and 149 | 24734 |
| 197 and 61 | 12017 |