Least Common Multiple (LCM) of 113 and 145
The least common multiple (LCM) of 113 and 145 is 16385.
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 145?
First, calculate the GCD of 113 and 145 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 145 = 0 remainder 113 |
| 2 | 145 ÷ 113 = 1 remainder 32 |
| 3 | 113 ÷ 32 = 3 remainder 17 |
| 4 | 32 ÷ 17 = 1 remainder 15 |
| 5 | 17 ÷ 15 = 1 remainder 2 |
| 6 | 15 ÷ 2 = 7 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 16 and 176 | 176 |
| 192 and 126 | 4032 |
| 24 and 130 | 1560 |
| 138 and 172 | 11868 |
| 107 and 139 | 14873 |