Least Common Multiple (LCM) of 108 and 40
The least common multiple (LCM) of 108 and 40 is 1080.
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 108 and 40?
First, calculate the GCD of 108 and 40 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 40 = 2 remainder 28 |
| 2 | 40 ÷ 28 = 1 remainder 12 |
| 3 | 28 ÷ 12 = 2 remainder 4 |
| 4 | 12 ÷ 4 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 47 | 5170 |
| 40 and 64 | 320 |
| 98 and 76 | 3724 |
| 102 and 40 | 2040 |
| 81 and 65 | 5265 |