Least Common Multiple (LCM) of 187 and 114
The least common multiple (LCM) of 187 and 114 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 187 and 114?
First, calculate the GCD of 187 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 187 ÷ 114 = 1 remainder 73 |
| 2 | 114 ÷ 73 = 1 remainder 41 |
| 3 | 73 ÷ 41 = 1 remainder 32 |
| 4 | 41 ÷ 32 = 1 remainder 9 |
| 5 | 32 ÷ 9 = 3 remainder 5 |
| 6 | 9 ÷ 5 = 1 remainder 4 |
| 7 | 5 ÷ 4 = 1 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 155 and 82 | 12710 |
| 122 and 123 | 15006 |
| 159 and 121 | 19239 |
| 84 and 23 | 1932 |
| 112 and 166 | 9296 |