Least Common Multiple (LCM) of 123 and 163
The least common multiple (LCM) of 123 and 163 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 123 and 163?
First, calculate the GCD of 123 and 163 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 163 = 0 remainder 123 |
| 2 | 163 ÷ 123 = 1 remainder 40 |
| 3 | 123 ÷ 40 = 3 remainder 3 |
| 4 | 40 ÷ 3 = 13 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 174 | 9570 |
| 200 and 37 | 7400 |
| 150 and 120 | 600 |
| 128 and 88 | 1408 |
| 90 and 154 | 6930 |