Least Common Multiple (LCM) of 144 and 123
The least common multiple (LCM) of 144 and 123 is 5904.
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 144 and 123?
First, calculate the GCD of 144 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 123 = 1 remainder 21 |
| 2 | 123 ÷ 21 = 5 remainder 18 |
| 3 | 21 ÷ 18 = 1 remainder 3 |
| 4 | 18 ÷ 3 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 151 and 162 | 24462 |
| 180 and 183 | 10980 |
| 168 and 116 | 4872 |
| 165 and 194 | 32010 |
| 90 and 20 | 180 |