Least Common Multiple (LCM) of 40 and 51
The least common multiple (LCM) of 40 and 51 is 2040.
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 51?
First, calculate the GCD of 40 and 51 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 51 = 0 remainder 40 |
| 2 | 51 ÷ 40 = 1 remainder 11 |
| 3 | 40 ÷ 11 = 3 remainder 7 |
| 4 | 11 ÷ 7 = 1 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 54 | 432 |
| 69 and 23 | 69 |
| 151 and 121 | 18271 |
| 171 and 21 | 1197 |
| 111 and 94 | 10434 |