Least Common Multiple (LCM) of 104 and 113
The least common multiple (LCM) of 104 and 113 is 11752.
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 104 and 113?
First, calculate the GCD of 104 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 104 ÷ 113 = 0 remainder 104 |
| 2 | 113 ÷ 104 = 1 remainder 9 |
| 3 | 104 ÷ 9 = 11 remainder 5 |
| 4 | 9 ÷ 5 = 1 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 111 and 178 | 19758 |
| 115 and 133 | 15295 |
| 67 and 90 | 6030 |
| 103 and 99 | 10197 |
| 135 and 55 | 1485 |