Least Common Multiple (LCM) of 46 and 102
The least common multiple (LCM) of 46 and 102 is 2346.
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 46 and 102?
First, calculate the GCD of 46 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 46 ÷ 102 = 0 remainder 46 |
| 2 | 102 ÷ 46 = 2 remainder 10 |
| 3 | 46 ÷ 10 = 4 remainder 6 |
| 4 | 10 ÷ 6 = 1 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 125 | 15375 |
| 111 and 21 | 777 |
| 177 and 150 | 8850 |
| 110 and 60 | 660 |
| 103 and 195 | 20085 |