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 |
|---|---|
| 107 and 185 | 19795 |
| 175 and 28 | 700 |
| 62 and 164 | 5084 |
| 179 and 81 | 14499 |
| 88 and 111 | 9768 |