Least Common Multiple (LCM) of 113 and 112
The least common multiple (LCM) of 113 and 112 is 12656.
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 113 and 112?
First, calculate the GCD of 113 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 112 = 1 remainder 1 |
| 2 | 112 ÷ 1 = 112 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 71 and 169 | 11999 |
| 105 and 84 | 420 |
| 105 and 178 | 18690 |
| 96 and 64 | 192 |
| 76 and 40 | 760 |