Least Common Multiple (LCM) of 104 and 119
The least common multiple (LCM) of 104 and 119 is 12376.
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 119?
First, calculate the GCD of 104 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 104 ÷ 119 = 0 remainder 104 |
| 2 | 119 ÷ 104 = 1 remainder 15 |
| 3 | 104 ÷ 15 = 6 remainder 14 |
| 4 | 15 ÷ 14 = 1 remainder 1 |
| 5 | 14 ÷ 1 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 77 and 177 | 13629 |
| 54 and 159 | 2862 |
| 37 and 65 | 2405 |
| 38 and 169 | 6422 |
| 114 and 32 | 1824 |