Least Common Multiple (LCM) of 46 and 118
The least common multiple (LCM) of 46 and 118 is 2714.
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 118?
First, calculate the GCD of 46 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 46 ÷ 118 = 0 remainder 46 |
| 2 | 118 ÷ 46 = 2 remainder 26 |
| 3 | 46 ÷ 26 = 1 remainder 20 |
| 4 | 26 ÷ 20 = 1 remainder 6 |
| 5 | 20 ÷ 6 = 3 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 142 | 18318 |
| 112 and 30 | 1680 |
| 60 and 36 | 180 |
| 192 and 159 | 10176 |
| 23 and 177 | 4071 |