Least Common Multiple (LCM) of 56 and 107
The least common multiple (LCM) of 56 and 107 is 5992.
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 107?
First, calculate the GCD of 56 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 56 ÷ 107 = 0 remainder 56 |
| 2 | 107 ÷ 56 = 1 remainder 51 |
| 3 | 56 ÷ 51 = 1 remainder 5 |
| 4 | 51 ÷ 5 = 10 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 180 | 2340 |
| 23 and 48 | 1104 |
| 106 and 149 | 15794 |
| 195 and 55 | 2145 |
| 123 and 97 | 11931 |