Least Common Multiple (LCM) of 105 and 93
The least common multiple (LCM) of 105 and 93 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 105 and 93?
First, calculate the GCD of 105 and 93 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 93 = 1 remainder 12 |
| 2 | 93 ÷ 12 = 7 remainder 9 |
| 3 | 12 ÷ 9 = 1 remainder 3 |
| 4 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 63 and 11 | 693 |
| 198 and 156 | 5148 |
| 67 and 86 | 5762 |
| 58 and 199 | 11542 |
| 20 and 110 | 220 |