Least Common Multiple (LCM) of 93 and 105
The least common multiple (LCM) of 93 and 105 is 3255.
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 105?
First, calculate the GCD of 93 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 93 ÷ 105 = 0 remainder 93 |
| 2 | 105 ÷ 93 = 1 remainder 12 |
| 3 | 93 ÷ 12 = 7 remainder 9 |
| 4 | 12 ÷ 9 = 1 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 103 | 11742 |
| 56 and 85 | 4760 |
| 194 and 81 | 15714 |
| 124 and 200 | 6200 |
| 158 and 133 | 21014 |