Least Common Multiple (LCM) of 19 and 167
The least common multiple (LCM) of 19 and 167 is 3173.
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 167?
First, calculate the GCD of 19 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 19 ÷ 167 = 0 remainder 19 |
| 2 | 167 ÷ 19 = 8 remainder 15 |
| 3 | 19 ÷ 15 = 1 remainder 4 |
| 4 | 15 ÷ 4 = 3 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 49 | 9408 |
| 57 and 41 | 2337 |
| 21 and 148 | 3108 |
| 191 and 124 | 23684 |
| 126 and 63 | 126 |