Least Common Multiple (LCM) of 46 and 116
The least common multiple (LCM) of 46 and 116 is 2668.
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 116?
First, calculate the GCD of 46 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 46 ÷ 116 = 0 remainder 46 |
| 2 | 116 ÷ 46 = 2 remainder 24 |
| 3 | 46 ÷ 24 = 1 remainder 22 |
| 4 | 24 ÷ 22 = 1 remainder 2 |
| 5 | 22 ÷ 2 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 168 and 132 | 1848 |
| 23 and 189 | 4347 |
| 187 and 84 | 15708 |
| 25 and 168 | 4200 |
| 115 and 120 | 2760 |