Least Common Multiple (LCM) of 113 and 19
The least common multiple (LCM) of 113 and 19 is 2147.
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 19?
First, calculate the GCD of 113 and 19 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 19 = 5 remainder 18 |
| 2 | 19 ÷ 18 = 1 remainder 1 |
| 3 | 18 ÷ 1 = 18 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 176 and 98 | 8624 |
| 139 and 153 | 21267 |
| 190 and 63 | 11970 |
| 174 and 88 | 7656 |
| 129 and 194 | 25026 |