Least Common Multiple (LCM) of 113 and 93
The least common multiple (LCM) of 113 and 93 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 113 and 93?
First, calculate the GCD of 113 and 93 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 93 = 1 remainder 20 |
| 2 | 93 ÷ 20 = 4 remainder 13 |
| 3 | 20 ÷ 13 = 1 remainder 7 |
| 4 | 13 ÷ 7 = 1 remainder 6 |
| 5 | 7 ÷ 6 = 1 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 31 | 4030 |
| 74 and 103 | 7622 |
| 194 and 162 | 15714 |
| 180 and 188 | 8460 |
| 176 and 145 | 25520 |