Least Common Multiple (LCM) of 52 and 96
The least common multiple (LCM) of 52 and 96 is 1248.
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 52 and 96?
First, calculate the GCD of 52 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 52 ÷ 96 = 0 remainder 52 |
| 2 | 96 ÷ 52 = 1 remainder 44 |
| 3 | 52 ÷ 44 = 1 remainder 8 |
| 4 | 44 ÷ 8 = 5 remainder 4 |
| 5 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 196 and 116 | 5684 |
| 197 and 139 | 27383 |
| 169 and 147 | 24843 |
| 148 and 196 | 7252 |
| 123 and 49 | 6027 |