Least Common Multiple (LCM) of 54 and 112
The least common multiple (LCM) of 54 and 112 is 3024.
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 112?
First, calculate the GCD of 54 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 112 = 0 remainder 54 |
| 2 | 112 ÷ 54 = 2 remainder 4 |
| 3 | 54 ÷ 4 = 13 remainder 2 |
| 4 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 161 and 68 | 10948 |
| 38 and 50 | 950 |
| 174 and 36 | 1044 |
| 68 and 195 | 13260 |
| 93 and 102 | 3162 |