Least Common Multiple (LCM) of 19 and 142
The least common multiple (LCM) of 19 and 142 is 2698.
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 142?
First, calculate the GCD of 19 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 19 ÷ 142 = 0 remainder 19 |
| 2 | 142 ÷ 19 = 7 remainder 9 |
| 3 | 19 ÷ 9 = 2 remainder 1 |
| 4 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 86 and 169 | 14534 |
| 111 and 82 | 9102 |
| 105 and 176 | 18480 |
| 12 and 12 | 12 |
| 13 and 70 | 910 |