Least Common Multiple (LCM) of 113 and 65
The least common multiple (LCM) of 113 and 65 is 7345.
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 65?
First, calculate the GCD of 113 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 65 = 1 remainder 48 |
| 2 | 65 ÷ 48 = 1 remainder 17 |
| 3 | 48 ÷ 17 = 2 remainder 14 |
| 4 | 17 ÷ 14 = 1 remainder 3 |
| 5 | 14 ÷ 3 = 4 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 171 | 5985 |
| 76 and 52 | 988 |
| 168 and 40 | 840 |
| 96 and 19 | 1824 |
| 51 and 117 | 1989 |