Least Common Multiple (LCM) of 114 and 159
The least common multiple (LCM) of 114 and 159 is 6042.
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 159?
First, calculate the GCD of 114 and 159 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 159 = 0 remainder 114 |
| 2 | 159 ÷ 114 = 1 remainder 45 |
| 3 | 114 ÷ 45 = 2 remainder 24 |
| 4 | 45 ÷ 24 = 1 remainder 21 |
| 5 | 24 ÷ 21 = 1 remainder 3 |
| 6 | 21 ÷ 3 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 99 and 81 | 891 |
| 76 and 171 | 684 |
| 110 and 143 | 1430 |
| 198 and 191 | 37818 |
| 20 and 110 | 220 |