Least Common Multiple (LCM) of 116 and 163
The least common multiple (LCM) of 116 and 163 is 18908.
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 163?
First, calculate the GCD of 116 and 163 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 163 = 0 remainder 116 |
| 2 | 163 ÷ 116 = 1 remainder 47 |
| 3 | 116 ÷ 47 = 2 remainder 22 |
| 4 | 47 ÷ 22 = 2 remainder 3 |
| 5 | 22 ÷ 3 = 7 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 132 | 1320 |
| 146 and 25 | 3650 |
| 14 and 110 | 770 |
| 110 and 111 | 12210 |
| 74 and 148 | 148 |