Least Common Multiple (LCM) of 96 and 53
The least common multiple (LCM) of 96 and 53 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 96 and 53?
First, calculate the GCD of 96 and 53 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 96 ÷ 53 = 1 remainder 43 |
| 2 | 53 ÷ 43 = 1 remainder 10 |
| 3 | 43 ÷ 10 = 4 remainder 3 |
| 4 | 10 ÷ 3 = 3 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 102 | 5406 |
| 41 and 117 | 4797 |
| 172 and 68 | 2924 |
| 185 and 35 | 1295 |
| 24 and 115 | 2760 |