Least Common Multiple (LCM) of 40 and 87
The least common multiple (LCM) of 40 and 87 is 3480.
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 87?
First, calculate the GCD of 40 and 87 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 87 = 0 remainder 40 |
| 2 | 87 ÷ 40 = 2 remainder 7 |
| 3 | 40 ÷ 7 = 5 remainder 5 |
| 4 | 7 ÷ 5 = 1 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 111 and 156 | 5772 |
| 114 and 174 | 3306 |
| 146 and 28 | 2044 |
| 114 and 94 | 5358 |
| 134 and 82 | 5494 |