Least Common Multiple (LCM) of 102 and 46
The least common multiple (LCM) of 102 and 46 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 102 and 46?
First, calculate the GCD of 102 and 46 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 46 = 2 remainder 10 |
| 2 | 46 ÷ 10 = 4 remainder 6 |
| 3 | 10 ÷ 6 = 1 remainder 4 |
| 4 | 6 ÷ 4 = 1 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 184 and 90 | 8280 |
| 112 and 137 | 15344 |
| 119 and 57 | 6783 |
| 76 and 65 | 4940 |
| 198 and 89 | 17622 |