Least Common Multiple (LCM) of 40 and 108
The least common multiple (LCM) of 40 and 108 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 40 and 108?
First, calculate the GCD of 40 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 108 = 0 remainder 40 |
| 2 | 108 ÷ 40 = 2 remainder 28 |
| 3 | 40 ÷ 28 = 1 remainder 12 |
| 4 | 28 ÷ 12 = 2 remainder 4 |
| 5 | 12 ÷ 4 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 162 and 170 | 13770 |
| 11 and 59 | 649 |
| 52 and 31 | 1612 |
| 114 and 179 | 20406 |
| 120 and 83 | 9960 |