Least Common Multiple (LCM) of 51 and 96
The least common multiple (LCM) of 51 and 96 is 1632.
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 51 and 96?
First, calculate the GCD of 51 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 51 ÷ 96 = 0 remainder 51 |
| 2 | 96 ÷ 51 = 1 remainder 45 |
| 3 | 51 ÷ 45 = 1 remainder 6 |
| 4 | 45 ÷ 6 = 7 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 89 | 10235 |
| 100 and 87 | 8700 |
| 120 and 85 | 2040 |
| 136 and 156 | 5304 |
| 122 and 76 | 4636 |