Least Common Multiple (LCM) of 93 and 109
The least common multiple (LCM) of 93 and 109 is 10137.
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 109?
First, calculate the GCD of 93 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 93 ÷ 109 = 0 remainder 93 |
| 2 | 109 ÷ 93 = 1 remainder 16 |
| 3 | 93 ÷ 16 = 5 remainder 13 |
| 4 | 16 ÷ 13 = 1 remainder 3 |
| 5 | 13 ÷ 3 = 4 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 75 | 675 |
| 87 and 151 | 13137 |
| 193 and 174 | 33582 |
| 154 and 178 | 13706 |
| 42 and 33 | 462 |