Least Common Multiple (LCM) of 84 and 96
The least common multiple (LCM) of 84 and 96 is 672.
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 84 and 96?
First, calculate the GCD of 84 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 84 ÷ 96 = 0 remainder 84 |
| 2 | 96 ÷ 84 = 1 remainder 12 |
| 3 | 84 ÷ 12 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 37 | 4070 |
| 77 and 40 | 3080 |
| 63 and 43 | 2709 |
| 94 and 94 | 94 |
| 165 and 80 | 2640 |