Least Common Multiple (LCM) of 105 and 187
The least common multiple (LCM) of 105 and 187 is 19635.
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 105 and 187?
First, calculate the GCD of 105 and 187 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 187 = 0 remainder 105 |
| 2 | 187 ÷ 105 = 1 remainder 82 |
| 3 | 105 ÷ 82 = 1 remainder 23 |
| 4 | 82 ÷ 23 = 3 remainder 13 |
| 5 | 23 ÷ 13 = 1 remainder 10 |
| 6 | 13 ÷ 10 = 1 remainder 3 |
| 7 | 10 ÷ 3 = 3 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 59 and 107 | 6313 |
| 31 and 70 | 2170 |
| 168 and 116 | 4872 |
| 96 and 59 | 5664 |
| 101 and 170 | 17170 |