Least Common Multiple (LCM) of 19 and 178
The least common multiple (LCM) of 19 and 178 is 3382.
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 178?
First, calculate the GCD of 19 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 19 ÷ 178 = 0 remainder 19 |
| 2 | 178 ÷ 19 = 9 remainder 7 |
| 3 | 19 ÷ 7 = 2 remainder 5 |
| 4 | 7 ÷ 5 = 1 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 24 | 336 |
| 117 and 180 | 2340 |
| 199 and 126 | 25074 |
| 161 and 151 | 24311 |
| 131 and 83 | 10873 |