Least Common Multiple (LCM) of 33 and 57
The least common multiple (LCM) of 33 and 57 is 627.
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 57?
First, calculate the GCD of 33 and 57 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 33 ÷ 57 = 0 remainder 33 |
| 2 | 57 ÷ 33 = 1 remainder 24 |
| 3 | 33 ÷ 24 = 1 remainder 9 |
| 4 | 24 ÷ 9 = 2 remainder 6 |
| 5 | 9 ÷ 6 = 1 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 148 and 151 | 22348 |
| 197 and 193 | 38021 |
| 126 and 177 | 7434 |
| 115 and 160 | 3680 |
| 97 and 65 | 6305 |