Least Common Multiple (LCM) of 56 and 78
The least common multiple (LCM) of 56 and 78 is 2184.
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 78?
First, calculate the GCD of 56 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 56 ÷ 78 = 0 remainder 56 |
| 2 | 78 ÷ 56 = 1 remainder 22 |
| 3 | 56 ÷ 22 = 2 remainder 12 |
| 4 | 22 ÷ 12 = 1 remainder 10 |
| 5 | 12 ÷ 10 = 1 remainder 2 |
| 6 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 65 and 170 | 2210 |
| 149 and 37 | 5513 |
| 150 and 74 | 5550 |
| 177 and 125 | 22125 |
| 173 and 145 | 25085 |