Least Common Multiple (LCM) of 56 and 185
The least common multiple (LCM) of 56 and 185 is 10360.
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 185?
First, calculate the GCD of 56 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 56 ÷ 185 = 0 remainder 56 |
| 2 | 185 ÷ 56 = 3 remainder 17 |
| 3 | 56 ÷ 17 = 3 remainder 5 |
| 4 | 17 ÷ 5 = 3 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 74 and 65 | 4810 |
| 75 and 68 | 5100 |
| 123 and 12 | 492 |
| 177 and 47 | 8319 |
| 21 and 192 | 1344 |