Least Common Multiple (LCM) of 54 and 38
The least common multiple (LCM) of 54 and 38 is 1026.
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 38?
First, calculate the GCD of 54 and 38 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 38 = 1 remainder 16 |
| 2 | 38 ÷ 16 = 2 remainder 6 |
| 3 | 16 ÷ 6 = 2 remainder 4 |
| 4 | 6 ÷ 4 = 1 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 70 and 54 | 1890 |
| 111 and 123 | 4551 |
| 120 and 23 | 2760 |
| 164 and 30 | 2460 |
| 122 and 123 | 15006 |