Least Common Multiple (LCM) of 96 and 111
The least common multiple (LCM) of 96 and 111 is 3552.
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 111?
First, calculate the GCD of 96 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 96 ÷ 111 = 0 remainder 96 |
| 2 | 111 ÷ 96 = 1 remainder 15 |
| 3 | 96 ÷ 15 = 6 remainder 6 |
| 4 | 15 ÷ 6 = 2 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 193 | 21616 |
| 182 and 147 | 3822 |
| 118 and 151 | 17818 |
| 132 and 123 | 5412 |
| 44 and 70 | 1540 |