Least Common Multiple (LCM) of 93 and 113
The least common multiple (LCM) of 93 and 113 is 10509.
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 113?
First, calculate the GCD of 93 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 93 ÷ 113 = 0 remainder 93 |
| 2 | 113 ÷ 93 = 1 remainder 20 |
| 3 | 93 ÷ 20 = 4 remainder 13 |
| 4 | 20 ÷ 13 = 1 remainder 7 |
| 5 | 13 ÷ 7 = 1 remainder 6 |
| 6 | 7 ÷ 6 = 1 remainder 1 |
| 7 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 22 | 1056 |
| 66 and 99 | 198 |
| 128 and 83 | 10624 |
| 90 and 40 | 360 |
| 185 and 24 | 4440 |