Least Common Multiple (LCM) of 111 and 187
The least common multiple (LCM) of 111 and 187 is 20757.
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 111 and 187?
First, calculate the GCD of 111 and 187 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 187 = 0 remainder 111 |
| 2 | 187 ÷ 111 = 1 remainder 76 |
| 3 | 111 ÷ 76 = 1 remainder 35 |
| 4 | 76 ÷ 35 = 2 remainder 6 |
| 5 | 35 ÷ 6 = 5 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 13 and 14 | 182 |
| 42 and 56 | 168 |
| 101 and 106 | 10706 |
| 134 and 169 | 22646 |
| 19 and 161 | 3059 |