Least Common Multiple (LCM) of 56 and 91
The least common multiple (LCM) of 56 and 91 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 91?
First, calculate the GCD of 56 and 91 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 56 ÷ 91 = 0 remainder 56 |
| 2 | 91 ÷ 56 = 1 remainder 35 |
| 3 | 56 ÷ 35 = 1 remainder 21 |
| 4 | 35 ÷ 21 = 1 remainder 14 |
| 5 | 21 ÷ 14 = 1 remainder 7 |
| 6 | 14 ÷ 7 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 190 | 2280 |
| 80 and 75 | 1200 |
| 200 and 57 | 11400 |
| 194 and 20 | 1940 |
| 46 and 42 | 966 |