Least Common Multiple (LCM) of 112 and 113
The least common multiple (LCM) of 112 and 113 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 112 and 113?
First, calculate the GCD of 112 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 113 = 0 remainder 112 |
| 2 | 113 ÷ 112 = 1 remainder 1 |
| 3 | 112 ÷ 1 = 112 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 157 and 72 | 11304 |
| 200 and 107 | 21400 |
| 188 and 136 | 6392 |
| 142 and 25 | 3550 |
| 77 and 167 | 12859 |