Least Common Multiple (LCM) of 33 and 93
The least common multiple (LCM) of 33 and 93 is 1023.
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 93?
First, calculate the GCD of 33 and 93 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 33 ÷ 93 = 0 remainder 33 |
| 2 | 93 ÷ 33 = 2 remainder 27 |
| 3 | 33 ÷ 27 = 1 remainder 6 |
| 4 | 27 ÷ 6 = 4 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 87 and 35 | 3045 |
| 157 and 114 | 17898 |
| 83 and 140 | 11620 |
| 182 and 196 | 2548 |
| 138 and 117 | 5382 |