Least Common Multiple (LCM) of 53 and 96
The least common multiple (LCM) of 53 and 96 is 5088.
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 53 and 96?
First, calculate the GCD of 53 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 96 = 0 remainder 53 |
| 2 | 96 ÷ 53 = 1 remainder 43 |
| 3 | 53 ÷ 43 = 1 remainder 10 |
| 4 | 43 ÷ 10 = 4 remainder 3 |
| 5 | 10 ÷ 3 = 3 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 54 and 151 | 8154 |
| 105 and 193 | 20265 |
| 34 and 82 | 1394 |
| 145 and 195 | 5655 |
| 169 and 149 | 25181 |