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 |
|---|---|
| 60 and 199 | 11940 |
| 77 and 114 | 8778 |
| 130 and 48 | 3120 |
| 63 and 29 | 1827 |
| 153 and 129 | 6579 |