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 |
|---|---|
| 21 and 89 | 1869 |
| 192 and 36 | 576 |
| 103 and 66 | 6798 |
| 30 and 31 | 930 |
| 160 and 112 | 1120 |