Least Common Multiple (LCM) of 115 and 113
The least common multiple (LCM) of 115 and 113 is 12995.
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 115 and 113?
First, calculate the GCD of 115 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 113 = 1 remainder 2 |
| 2 | 113 ÷ 2 = 56 remainder 1 |
| 3 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 176 and 20 | 880 |
| 71 and 16 | 1136 |
| 157 and 164 | 25748 |
| 145 and 173 | 25085 |
| 137 and 75 | 10275 |