Least Common Multiple (LCM) of 56 and 104
The least common multiple (LCM) of 56 and 104 is 728.
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 104?
First, calculate the GCD of 56 and 104 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 56 ÷ 104 = 0 remainder 56 |
| 2 | 104 ÷ 56 = 1 remainder 48 |
| 3 | 56 ÷ 48 = 1 remainder 8 |
| 4 | 48 ÷ 8 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 194 and 109 | 21146 |
| 41 and 20 | 820 |
| 114 and 183 | 6954 |
| 31 and 192 | 5952 |
| 121 and 156 | 18876 |