Least Common Multiple (LCM) of 144 and 56
The least common multiple (LCM) of 144 and 56 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 144 and 56?
First, calculate the GCD of 144 and 56 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 56 = 2 remainder 32 |
| 2 | 56 ÷ 32 = 1 remainder 24 |
| 3 | 32 ÷ 24 = 1 remainder 8 |
| 4 | 24 ÷ 8 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 58 and 59 | 3422 |
| 28 and 104 | 728 |
| 39 and 87 | 1131 |
| 113 and 15 | 1695 |
| 20 and 60 | 60 |