Least Common Multiple (LCM) of 46 and 164
The least common multiple (LCM) of 46 and 164 is 3772.
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 164?
First, calculate the GCD of 46 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 46 ÷ 164 = 0 remainder 46 |
| 2 | 164 ÷ 46 = 3 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 |
|---|---|
| 13 and 197 | 2561 |
| 147 and 109 | 16023 |
| 54 and 182 | 4914 |
| 114 and 81 | 3078 |
| 69 and 57 | 1311 |