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 |
|---|---|
| 127 and 99 | 12573 |
| 31 and 79 | 2449 |
| 148 and 189 | 27972 |
| 44 and 68 | 748 |
| 36 and 67 | 2412 |