Least Common Multiple (LCM) of 19 and 114
The least common multiple (LCM) of 19 and 114 is 114.
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 19 and 114?
First, calculate the GCD of 19 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 19 ÷ 114 = 0 remainder 19 |
| 2 | 114 ÷ 19 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 190 | 13680 |
| 191 and 133 | 25403 |
| 106 and 165 | 17490 |
| 163 and 20 | 3260 |
| 162 and 105 | 5670 |