Least Common Multiple (LCM) of 102 and 43
The least common multiple (LCM) of 102 and 43 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 102 and 43?
First, calculate the GCD of 102 and 43 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 43 = 2 remainder 16 |
| 2 | 43 ÷ 16 = 2 remainder 11 |
| 3 | 16 ÷ 11 = 1 remainder 5 |
| 4 | 11 ÷ 5 = 2 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 51 | 5457 |
| 113 and 147 | 16611 |
| 121 and 133 | 16093 |
| 87 and 29 | 87 |
| 162 and 151 | 24462 |