Least Common Multiple (LCM) of 56 and 41
The least common multiple (LCM) of 56 and 41 is 2296.
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 41?
First, calculate the GCD of 56 and 41 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 56 ÷ 41 = 1 remainder 15 |
| 2 | 41 ÷ 15 = 2 remainder 11 |
| 3 | 15 ÷ 11 = 1 remainder 4 |
| 4 | 11 ÷ 4 = 2 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 185 and 184 | 34040 |
| 103 and 178 | 18334 |
| 160 and 140 | 1120 |
| 160 and 15 | 480 |
| 85 and 20 | 340 |