Least Common Multiple (LCM) of 40 and 66
The least common multiple (LCM) of 40 and 66 is 1320.
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 66?
First, calculate the GCD of 40 and 66 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 66 = 0 remainder 40 |
| 2 | 66 ÷ 40 = 1 remainder 26 |
| 3 | 40 ÷ 26 = 1 remainder 14 |
| 4 | 26 ÷ 14 = 1 remainder 12 |
| 5 | 14 ÷ 12 = 1 remainder 2 |
| 6 | 12 ÷ 2 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 73 | 8249 |
| 66 and 116 | 3828 |
| 148 and 71 | 10508 |
| 128 and 61 | 7808 |
| 119 and 162 | 19278 |