Least Common Multiple (LCM) of 112 and 54
The least common multiple (LCM) of 112 and 54 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 112 and 54?
First, calculate the GCD of 112 and 54 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 54 = 2 remainder 4 |
| 2 | 54 ÷ 4 = 13 remainder 2 |
| 3 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 116 and 30 | 1740 |
| 100 and 11 | 1100 |
| 77 and 149 | 11473 |
| 88 and 100 | 2200 |
| 27 and 137 | 3699 |