Least Common Multiple (LCM) of 56 and 92
The least common multiple (LCM) of 56 and 92 is 1288.
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 92?
First, calculate the GCD of 56 and 92 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 56 ÷ 92 = 0 remainder 56 |
| 2 | 92 ÷ 56 = 1 remainder 36 |
| 3 | 56 ÷ 36 = 1 remainder 20 |
| 4 | 36 ÷ 20 = 1 remainder 16 |
| 5 | 20 ÷ 16 = 1 remainder 4 |
| 6 | 16 ÷ 4 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 40 | 560 |
| 107 and 107 | 107 |
| 190 and 47 | 8930 |
| 109 and 196 | 21364 |
| 31 and 146 | 4526 |