Least Common Multiple (LCM) of 112 and 144
The least common multiple (LCM) of 112 and 144 is 1008.
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 144?
First, calculate the GCD of 112 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 144 = 0 remainder 112 |
| 2 | 144 ÷ 112 = 1 remainder 32 |
| 3 | 112 ÷ 32 = 3 remainder 16 |
| 4 | 32 ÷ 16 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 118 and 132 | 7788 |
| 125 and 69 | 8625 |
| 109 and 77 | 8393 |
| 195 and 183 | 11895 |
| 182 and 102 | 9282 |