Least Common Multiple (LCM) of 96 and 69
The least common multiple (LCM) of 96 and 69 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 96 and 69?
First, calculate the GCD of 96 and 69 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 96 ÷ 69 = 1 remainder 27 |
| 2 | 69 ÷ 27 = 2 remainder 15 |
| 3 | 27 ÷ 15 = 1 remainder 12 |
| 4 | 15 ÷ 12 = 1 remainder 3 |
| 5 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 102 | 11526 |
| 10 and 73 | 730 |
| 180 and 55 | 1980 |
| 127 and 106 | 13462 |
| 13 and 28 | 364 |