Least Common Multiple (LCM) of 10 and 19
The least common multiple (LCM) of 10 and 19 is 190.
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 10 and 19?
First, calculate the GCD of 10 and 19 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 10 ÷ 19 = 0 remainder 10 |
| 2 | 19 ÷ 10 = 1 remainder 9 |
| 3 | 10 ÷ 9 = 1 remainder 1 |
| 4 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 34 and 156 | 2652 |
| 198 and 119 | 23562 |
| 108 and 19 | 2052 |
| 89 and 85 | 7565 |
| 188 and 22 | 2068 |