Least Common Multiple (LCM) of 114 and 45
The least common multiple (LCM) of 114 and 45 is 1710.
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 45?
First, calculate the GCD of 114 and 45 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 45 = 2 remainder 24 |
| 2 | 45 ÷ 24 = 1 remainder 21 |
| 3 | 24 ÷ 21 = 1 remainder 3 |
| 4 | 21 ÷ 3 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 50 and 104 | 2600 |
| 34 and 35 | 1190 |
| 39 and 189 | 2457 |
| 191 and 186 | 35526 |
| 12 and 47 | 564 |