Least Common Multiple (LCM) of 55 and 96
The least common multiple (LCM) of 55 and 96 is 5280.
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 55 and 96?
First, calculate the GCD of 55 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 55 ÷ 96 = 0 remainder 55 |
| 2 | 96 ÷ 55 = 1 remainder 41 |
| 3 | 55 ÷ 41 = 1 remainder 14 |
| 4 | 41 ÷ 14 = 2 remainder 13 |
| 5 | 14 ÷ 13 = 1 remainder 1 |
| 6 | 13 ÷ 1 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 18 | 1170 |
| 106 and 149 | 15794 |
| 163 and 17 | 2771 |
| 56 and 122 | 3416 |
| 181 and 165 | 29865 |