Least Common Multiple (LCM) of 105 and 40
The least common multiple (LCM) of 105 and 40 is 840.
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 105 and 40?
First, calculate the GCD of 105 and 40 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 40 = 2 remainder 25 |
| 2 | 40 ÷ 25 = 1 remainder 15 |
| 3 | 25 ÷ 15 = 1 remainder 10 |
| 4 | 15 ÷ 10 = 1 remainder 5 |
| 5 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 81 and 167 | 13527 |
| 85 and 108 | 9180 |
| 54 and 67 | 3618 |
| 113 and 95 | 10735 |
| 142 and 91 | 12922 |