Least Common Multiple (LCM) of 123 and 44
The least common multiple (LCM) of 123 and 44 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 123 and 44?
First, calculate the GCD of 123 and 44 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 44 = 2 remainder 35 |
| 2 | 44 ÷ 35 = 1 remainder 9 |
| 3 | 35 ÷ 9 = 3 remainder 8 |
| 4 | 9 ÷ 8 = 1 remainder 1 |
| 5 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 34 and 51 | 102 |
| 45 and 158 | 7110 |
| 111 and 151 | 16761 |
| 89 and 148 | 13172 |
| 175 and 49 | 1225 |