Least Common Multiple (LCM) of 40 and 73
The least common multiple (LCM) of 40 and 73 is 2920.
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 73?
First, calculate the GCD of 40 and 73 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 73 = 0 remainder 40 |
| 2 | 73 ÷ 40 = 1 remainder 33 |
| 3 | 40 ÷ 33 = 1 remainder 7 |
| 4 | 33 ÷ 7 = 4 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 163 and 131 | 21353 |
| 115 and 157 | 18055 |
| 42 and 14 | 42 |
| 191 and 62 | 11842 |
| 22 and 166 | 1826 |