Least Common Multiple (LCM) of 44 and 123
The least common multiple (LCM) of 44 and 123 is 5412.
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 44 and 123?
First, calculate the GCD of 44 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 44 ÷ 123 = 0 remainder 44 |
| 2 | 123 ÷ 44 = 2 remainder 35 |
| 3 | 44 ÷ 35 = 1 remainder 9 |
| 4 | 35 ÷ 9 = 3 remainder 8 |
| 5 | 9 ÷ 8 = 1 remainder 1 |
| 6 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 196 and 192 | 9408 |
| 79 and 84 | 6636 |
| 44 and 40 | 440 |
| 72 and 24 | 72 |
| 196 and 169 | 33124 |