Least Common Multiple (LCM) of 93 and 112
The least common multiple (LCM) of 93 and 112 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 93 and 112?
First, calculate the GCD of 93 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 93 ÷ 112 = 0 remainder 93 |
| 2 | 112 ÷ 93 = 1 remainder 19 |
| 3 | 93 ÷ 19 = 4 remainder 17 |
| 4 | 19 ÷ 17 = 1 remainder 2 |
| 5 | 17 ÷ 2 = 8 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 59 | 7257 |
| 154 and 158 | 12166 |
| 112 and 72 | 1008 |
| 69 and 198 | 4554 |
| 68 and 181 | 12308 |