Least Common Multiple (LCM) of 33 and 40
The least common multiple (LCM) of 33 and 40 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 33 and 40?
First, calculate the GCD of 33 and 40 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 33 ÷ 40 = 0 remainder 33 |
| 2 | 40 ÷ 33 = 1 remainder 7 |
| 3 | 33 ÷ 7 = 4 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 |
|---|---|
| 187 and 118 | 22066 |
| 152 and 45 | 6840 |
| 39 and 40 | 1560 |
| 27 and 103 | 2781 |
| 105 and 90 | 630 |