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 |
|---|---|
| 195 and 164 | 31980 |
| 75 and 76 | 5700 |
| 53 and 187 | 9911 |
| 90 and 125 | 2250 |
| 168 and 196 | 1176 |