Least Common Multiple (LCM) of 19 and 176
The least common multiple (LCM) of 19 and 176 is 3344.
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 176?
First, calculate the GCD of 19 and 176 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 19 ÷ 176 = 0 remainder 19 |
| 2 | 176 ÷ 19 = 9 remainder 5 |
| 3 | 19 ÷ 5 = 3 remainder 4 |
| 4 | 5 ÷ 4 = 1 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 42 | 4578 |
| 114 and 45 | 1710 |
| 40 and 35 | 280 |
| 83 and 107 | 8881 |
| 192 and 25 | 4800 |