Least Common Multiple (LCM) of 46 and 54
The least common multiple (LCM) of 46 and 54 is 1242.
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 54?
First, calculate the GCD of 46 and 54 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 46 ÷ 54 = 0 remainder 46 |
| 2 | 54 ÷ 46 = 1 remainder 8 |
| 3 | 46 ÷ 8 = 5 remainder 6 |
| 4 | 8 ÷ 6 = 1 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 25 | 425 |
| 144 and 15 | 720 |
| 18 and 155 | 2790 |
| 32 and 105 | 3360 |
| 106 and 27 | 2862 |