Least Common Multiple (LCM) of 114 and 187
The least common multiple (LCM) of 114 and 187 is 21318.
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 114 and 187?
First, calculate the GCD of 114 and 187 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 187 = 0 remainder 114 |
| 2 | 187 ÷ 114 = 1 remainder 73 |
| 3 | 114 ÷ 73 = 1 remainder 41 |
| 4 | 73 ÷ 41 = 1 remainder 32 |
| 5 | 41 ÷ 32 = 1 remainder 9 |
| 6 | 32 ÷ 9 = 3 remainder 5 |
| 7 | 9 ÷ 5 = 1 remainder 4 |
| 8 | 5 ÷ 4 = 1 remainder 1 |
| 9 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 34 and 71 | 2414 |
| 130 and 156 | 780 |
| 173 and 125 | 21625 |
| 116 and 11 | 1276 |
| 159 and 103 | 16377 |