Least Common Multiple (LCM) of 54 and 123
The least common multiple (LCM) of 54 and 123 is 2214.
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 54 and 123?
First, calculate the GCD of 54 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 123 = 0 remainder 54 |
| 2 | 123 ÷ 54 = 2 remainder 15 |
| 3 | 54 ÷ 15 = 3 remainder 9 |
| 4 | 15 ÷ 9 = 1 remainder 6 |
| 5 | 9 ÷ 6 = 1 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 188 and 163 | 30644 |
| 189 and 68 | 12852 |
| 131 and 21 | 2751 |
| 105 and 182 | 2730 |
| 156 and 129 | 6708 |