Least Common Multiple (LCM) of 112 and 93
The least common multiple (LCM) of 112 and 93 is 10416.
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 112 and 93?
First, calculate the GCD of 112 and 93 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 93 = 1 remainder 19 |
| 2 | 93 ÷ 19 = 4 remainder 17 |
| 3 | 19 ÷ 17 = 1 remainder 2 |
| 4 | 17 ÷ 2 = 8 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 88 | 2112 |
| 121 and 42 | 5082 |
| 70 and 180 | 1260 |
| 26 and 89 | 2314 |
| 31 and 128 | 3968 |