Least Common Multiple (LCM) of 46 and 144
The least common multiple (LCM) of 46 and 144 is 3312.
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 144?
First, calculate the GCD of 46 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 46 ÷ 144 = 0 remainder 46 |
| 2 | 144 ÷ 46 = 3 remainder 6 |
| 3 | 46 ÷ 6 = 7 remainder 4 |
| 4 | 6 ÷ 4 = 1 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 17 | 102 |
| 80 and 161 | 12880 |
| 114 and 129 | 4902 |
| 85 and 68 | 340 |
| 20 and 78 | 780 |