Least Common Multiple (LCM) of 99 and 112
The least common multiple (LCM) of 99 and 112 is 11088.
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 99 and 112?
First, calculate the GCD of 99 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 112 = 0 remainder 99 |
| 2 | 112 ÷ 99 = 1 remainder 13 |
| 3 | 99 ÷ 13 = 7 remainder 8 |
| 4 | 13 ÷ 8 = 1 remainder 5 |
| 5 | 8 ÷ 5 = 1 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 51 and 22 | 1122 |
| 186 and 108 | 3348 |
| 86 and 49 | 4214 |
| 33 and 105 | 1155 |
| 25 and 140 | 700 |