Least Common Multiple (LCM) of 109 and 93
The least common multiple (LCM) of 109 and 93 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 109 and 93?
First, calculate the GCD of 109 and 93 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 93 = 1 remainder 16 |
| 2 | 93 ÷ 16 = 5 remainder 13 |
| 3 | 16 ÷ 13 = 1 remainder 3 |
| 4 | 13 ÷ 3 = 4 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 148 and 78 | 5772 |
| 92 and 41 | 3772 |
| 34 and 164 | 2788 |
| 30 and 59 | 1770 |
| 139 and 161 | 22379 |