Least Common Multiple (LCM) of 30 and 112
The least common multiple (LCM) of 30 and 112 is 1680.
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 30 and 112?
First, calculate the GCD of 30 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 112 = 0 remainder 30 |
| 2 | 112 ÷ 30 = 3 remainder 22 |
| 3 | 30 ÷ 22 = 1 remainder 8 |
| 4 | 22 ÷ 8 = 2 remainder 6 |
| 5 | 8 ÷ 6 = 1 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 186 and 78 | 2418 |
| 16 and 131 | 2096 |
| 20 and 166 | 1660 |
| 22 and 75 | 1650 |
| 60 and 156 | 780 |