Least Common Multiple (LCM) of 56 and 85
The least common multiple (LCM) of 56 and 85 is 4760.
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 85?
First, calculate the GCD of 56 and 85 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 56 ÷ 85 = 0 remainder 56 |
| 2 | 85 ÷ 56 = 1 remainder 29 |
| 3 | 56 ÷ 29 = 1 remainder 27 |
| 4 | 29 ÷ 27 = 1 remainder 2 |
| 5 | 27 ÷ 2 = 13 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 79 and 143 | 11297 |
| 108 and 200 | 5400 |
| 195 and 188 | 36660 |
| 161 and 159 | 25599 |
| 13 and 17 | 221 |