Least Common Multiple (LCM) of 108 and 112
The least common multiple (LCM) of 108 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 108 and 112?
First, calculate the GCD of 108 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 112 = 0 remainder 108 |
| 2 | 112 ÷ 108 = 1 remainder 4 |
| 3 | 108 ÷ 4 = 27 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 141 | 4512 |
| 102 and 38 | 1938 |
| 165 and 101 | 16665 |
| 189 and 96 | 6048 |
| 38 and 14 | 266 |