Least Common Multiple (LCM) of 33 and 64
The least common multiple (LCM) of 33 and 64 is 2112.
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 64?
First, calculate the GCD of 33 and 64 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 33 ÷ 64 = 0 remainder 33 |
| 2 | 64 ÷ 33 = 1 remainder 31 |
| 3 | 33 ÷ 31 = 1 remainder 2 |
| 4 | 31 ÷ 2 = 15 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 49 and 59 | 2891 |
| 30 and 192 | 960 |
| 140 and 86 | 6020 |
| 16 and 112 | 112 |
| 190 and 69 | 13110 |