Least Common Multiple (LCM) of 112 and 115
The least common multiple (LCM) of 112 and 115 is 12880.
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 115?
First, calculate the GCD of 112 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 115 = 0 remainder 112 |
| 2 | 115 ÷ 112 = 1 remainder 3 |
| 3 | 112 ÷ 3 = 37 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 71 | 9727 |
| 21 and 165 | 1155 |
| 37 and 174 | 6438 |
| 119 and 165 | 19635 |
| 109 and 119 | 12971 |