Least Common Multiple (LCM) of 68 and 96
The least common multiple (LCM) of 68 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 68 and 96?
First, calculate the GCD of 68 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 96 = 0 remainder 68 |
| 2 | 96 ÷ 68 = 1 remainder 28 |
| 3 | 68 ÷ 28 = 2 remainder 12 |
| 4 | 28 ÷ 12 = 2 remainder 4 |
| 5 | 12 ÷ 4 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 84 | 3276 |
| 58 and 35 | 2030 |
| 80 and 67 | 5360 |
| 107 and 94 | 10058 |
| 108 and 165 | 5940 |