Least Common Multiple (LCM) of 163 and 111
The least common multiple (LCM) of 163 and 111 is 18093.
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 163 and 111?
First, calculate the GCD of 163 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 163 ÷ 111 = 1 remainder 52 |
| 2 | 111 ÷ 52 = 2 remainder 7 |
| 3 | 52 ÷ 7 = 7 remainder 3 |
| 4 | 7 ÷ 3 = 2 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 121 and 178 | 21538 |
| 21 and 135 | 945 |
| 23 and 195 | 4485 |
| 30 and 139 | 4170 |
| 138 and 14 | 966 |