Least Common Multiple (LCM) of 46 and 178
The least common multiple (LCM) of 46 and 178 is 4094.
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 178?
First, calculate the GCD of 46 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 46 ÷ 178 = 0 remainder 46 |
| 2 | 178 ÷ 46 = 3 remainder 40 |
| 3 | 46 ÷ 40 = 1 remainder 6 |
| 4 | 40 ÷ 6 = 6 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 72 | 3816 |
| 82 and 64 | 2624 |
| 176 and 92 | 4048 |
| 148 and 133 | 19684 |
| 67 and 47 | 3149 |