Least Common Multiple (LCM) of 78 and 56
The least common multiple (LCM) of 78 and 56 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 78 and 56?
First, calculate the GCD of 78 and 56 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 56 = 1 remainder 22 |
| 2 | 56 ÷ 22 = 2 remainder 12 |
| 3 | 22 ÷ 12 = 1 remainder 10 |
| 4 | 12 ÷ 10 = 1 remainder 2 |
| 5 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 14 | 1806 |
| 199 and 69 | 13731 |
| 84 and 35 | 420 |
| 17 and 160 | 2720 |
| 93 and 198 | 6138 |