Least Common Multiple (LCM) of 113 and 64
The least common multiple (LCM) of 113 and 64 is 7232.
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 64?
First, calculate the GCD of 113 and 64 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 64 = 1 remainder 49 |
| 2 | 64 ÷ 49 = 1 remainder 15 |
| 3 | 49 ÷ 15 = 3 remainder 4 |
| 4 | 15 ÷ 4 = 3 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 48 and 131 | 6288 |
| 21 and 109 | 2289 |
| 123 and 185 | 22755 |
| 173 and 130 | 22490 |
| 20 and 147 | 2940 |