Least Common Multiple (LCM) of 43 and 102
The least common multiple (LCM) of 43 and 102 is 4386.
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 43 and 102?
First, calculate the GCD of 43 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 43 ÷ 102 = 0 remainder 43 |
| 2 | 102 ÷ 43 = 2 remainder 16 |
| 3 | 43 ÷ 16 = 2 remainder 11 |
| 4 | 16 ÷ 11 = 1 remainder 5 |
| 5 | 11 ÷ 5 = 2 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 68 | 7956 |
| 101 and 153 | 15453 |
| 17 and 159 | 2703 |
| 139 and 126 | 17514 |
| 119 and 104 | 12376 |