Least Common Multiple (LCM) of 40 and 104
The least common multiple (LCM) of 40 and 104 is 520.
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 40 and 104?
First, calculate the GCD of 40 and 104 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 104 = 0 remainder 40 |
| 2 | 104 ÷ 40 = 2 remainder 24 |
| 3 | 40 ÷ 24 = 1 remainder 16 |
| 4 | 24 ÷ 16 = 1 remainder 8 |
| 5 | 16 ÷ 8 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 104 and 32 | 416 |
| 124 and 107 | 13268 |
| 199 and 35 | 6965 |
| 174 and 152 | 13224 |
| 65 and 109 | 7085 |