Least Common Multiple (LCM) of 123 and 144
The least common multiple (LCM) of 123 and 144 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 123 and 144?
First, calculate the GCD of 123 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 144 = 0 remainder 123 |
| 2 | 144 ÷ 123 = 1 remainder 21 |
| 3 | 123 ÷ 21 = 5 remainder 18 |
| 4 | 21 ÷ 18 = 1 remainder 3 |
| 5 | 18 ÷ 3 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 189 | 7182 |
| 105 and 74 | 7770 |
| 77 and 16 | 1232 |
| 26 and 62 | 806 |
| 184 and 13 | 2392 |