Least Common Multiple (LCM) of 67 and 96
The least common multiple (LCM) of 67 and 96 is 6432.
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 67 and 96?
First, calculate the GCD of 67 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 96 = 0 remainder 67 |
| 2 | 96 ÷ 67 = 1 remainder 29 |
| 3 | 67 ÷ 29 = 2 remainder 9 |
| 4 | 29 ÷ 9 = 3 remainder 2 |
| 5 | 9 ÷ 2 = 4 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 131 and 137 | 17947 |
| 153 and 47 | 7191 |
| 22 and 178 | 1958 |
| 51 and 68 | 204 |
| 17 and 158 | 2686 |