Least Common Multiple (LCM) of 113 and 103
The least common multiple (LCM) of 113 and 103 is 11639.
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 103?
First, calculate the GCD of 113 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 103 = 1 remainder 10 |
| 2 | 103 ÷ 10 = 10 remainder 3 |
| 3 | 10 ÷ 3 = 3 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 101 and 43 | 4343 |
| 57 and 141 | 2679 |
| 73 and 196 | 14308 |
| 180 and 144 | 720 |
| 71 and 31 | 2201 |