Least Common Multiple (LCM) of 72 and 96
The least common multiple (LCM) of 72 and 96 is 288.
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 72 and 96?
First, calculate the GCD of 72 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 96 = 0 remainder 72 |
| 2 | 96 ÷ 72 = 1 remainder 24 |
| 3 | 72 ÷ 24 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 133 | 13699 |
| 105 and 174 | 6090 |
| 100 and 88 | 2200 |
| 172 and 13 | 2236 |
| 177 and 185 | 32745 |