Least Common Multiple (LCM) of 112 and 66
The least common multiple (LCM) of 112 and 66 is 3696.
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 66?
First, calculate the GCD of 112 and 66 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 66 = 1 remainder 46 |
| 2 | 66 ÷ 46 = 1 remainder 20 |
| 3 | 46 ÷ 20 = 2 remainder 6 |
| 4 | 20 ÷ 6 = 3 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 165 | 7920 |
| 65 and 173 | 11245 |
| 130 and 173 | 22490 |
| 174 and 149 | 25926 |
| 199 and 130 | 25870 |