Least Common Multiple (LCM) of 96 and 182
The least common multiple (LCM) of 96 and 182 is 8736.
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 182?
First, calculate the GCD of 96 and 182 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 96 ÷ 182 = 0 remainder 96 |
| 2 | 182 ÷ 96 = 1 remainder 86 |
| 3 | 96 ÷ 86 = 1 remainder 10 |
| 4 | 86 ÷ 10 = 8 remainder 6 |
| 5 | 10 ÷ 6 = 1 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 106 | 7420 |
| 107 and 160 | 17120 |
| 27 and 180 | 540 |
| 137 and 111 | 15207 |
| 85 and 147 | 12495 |