Least Common Multiple (LCM) of 112 and 46
The least common multiple (LCM) of 112 and 46 is 2576.
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 46?
First, calculate the GCD of 112 and 46 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 46 = 2 remainder 20 |
| 2 | 46 ÷ 20 = 2 remainder 6 |
| 3 | 20 ÷ 6 = 3 remainder 2 |
| 4 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 161 and 69 | 483 |
| 174 and 100 | 8700 |
| 58 and 174 | 174 |
| 32 and 131 | 4192 |
| 115 and 96 | 11040 |