Least Common Multiple (LCM) of 19 and 187
The least common multiple (LCM) of 19 and 187 is 3553.
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 187?
First, calculate the GCD of 19 and 187 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 19 ÷ 187 = 0 remainder 19 |
| 2 | 187 ÷ 19 = 9 remainder 16 |
| 3 | 19 ÷ 16 = 1 remainder 3 |
| 4 | 16 ÷ 3 = 5 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 124 and 75 | 9300 |
| 84 and 29 | 2436 |
| 195 and 193 | 37635 |
| 17 and 75 | 1275 |
| 110 and 111 | 12210 |