Least Common Multiple (LCM) of 104 and 149
The least common multiple (LCM) of 104 and 149 is 15496.
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 149?
First, calculate the GCD of 104 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 104 ÷ 149 = 0 remainder 104 |
| 2 | 149 ÷ 104 = 1 remainder 45 |
| 3 | 104 ÷ 45 = 2 remainder 14 |
| 4 | 45 ÷ 14 = 3 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 |
|---|---|
| 57 and 68 | 3876 |
| 170 and 21 | 3570 |
| 196 and 181 | 35476 |
| 199 and 178 | 35422 |
| 13 and 199 | 2587 |