Least Common Multiple (LCM) of 69 and 96
The least common multiple (LCM) of 69 and 96 is 2208.
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 69 and 96?
First, calculate the GCD of 69 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 96 = 0 remainder 69 |
| 2 | 96 ÷ 69 = 1 remainder 27 |
| 3 | 69 ÷ 27 = 2 remainder 15 |
| 4 | 27 ÷ 15 = 1 remainder 12 |
| 5 | 15 ÷ 12 = 1 remainder 3 |
| 6 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 195 and 41 | 7995 |
| 160 and 40 | 160 |
| 123 and 150 | 6150 |
| 187 and 32 | 5984 |
| 138 and 36 | 828 |