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 |
|---|---|
| 16 and 157 | 2512 |
| 196 and 185 | 36260 |
| 121 and 83 | 10043 |
| 99 and 49 | 4851 |
| 48 and 185 | 8880 |