Least Common Multiple (LCM) of 163 and 123
The least common multiple (LCM) of 163 and 123 is 20049.
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 123?
First, calculate the GCD of 163 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 163 ÷ 123 = 1 remainder 40 |
| 2 | 123 ÷ 40 = 3 remainder 3 |
| 3 | 40 ÷ 3 = 13 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 161 and 41 | 6601 |
| 111 and 64 | 7104 |
| 24 and 32 | 96 |
| 135 and 15 | 135 |
| 197 and 11 | 2167 |