Least Common Multiple (LCM) of 56 and 144
The least common multiple (LCM) of 56 and 144 is 1008.
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 56 and 144?
First, calculate the GCD of 56 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 56 ÷ 144 = 0 remainder 56 |
| 2 | 144 ÷ 56 = 2 remainder 32 |
| 3 | 56 ÷ 32 = 1 remainder 24 |
| 4 | 32 ÷ 24 = 1 remainder 8 |
| 5 | 24 ÷ 8 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 54 and 52 | 1404 |
| 107 and 199 | 21293 |
| 105 and 123 | 4305 |
| 47 and 154 | 7238 |
| 150 and 25 | 150 |