Least Common Multiple (LCM) of 13 and 187
The least common multiple (LCM) of 13 and 187 is 2431.
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 13 and 187?
First, calculate the GCD of 13 and 187 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 13 ÷ 187 = 0 remainder 13 |
| 2 | 187 ÷ 13 = 14 remainder 5 |
| 3 | 13 ÷ 5 = 2 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 153 and 86 | 13158 |
| 99 and 85 | 8415 |
| 134 and 27 | 3618 |
| 184 and 125 | 23000 |
| 179 and 35 | 6265 |