Least Common Multiple (LCM) of 116 and 101
The least common multiple (LCM) of 116 and 101 is 11716.
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 101?
First, calculate the GCD of 116 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 101 = 1 remainder 15 |
| 2 | 101 ÷ 15 = 6 remainder 11 |
| 3 | 15 ÷ 11 = 1 remainder 4 |
| 4 | 11 ÷ 4 = 2 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 151 and 41 | 6191 |
| 94 and 121 | 11374 |
| 173 and 19 | 3287 |
| 16 and 183 | 2928 |
| 168 and 169 | 28392 |