Least Common Multiple (LCM) of 114 and 43
The least common multiple (LCM) of 114 and 43 is 4902.
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 43?
First, calculate the GCD of 114 and 43 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 43 = 2 remainder 28 |
| 2 | 43 ÷ 28 = 1 remainder 15 |
| 3 | 28 ÷ 15 = 1 remainder 13 |
| 4 | 15 ÷ 13 = 1 remainder 2 |
| 5 | 13 ÷ 2 = 6 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 35 and 165 | 1155 |
| 146 and 88 | 6424 |
| 39 and 102 | 1326 |
| 106 and 83 | 8798 |
| 58 and 138 | 4002 |