Least Common Multiple (LCM) of 33 and 52
The least common multiple (LCM) of 33 and 52 is 1716.
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 52?
First, calculate the GCD of 33 and 52 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 33 ÷ 52 = 0 remainder 33 |
| 2 | 52 ÷ 33 = 1 remainder 19 |
| 3 | 33 ÷ 19 = 1 remainder 14 |
| 4 | 19 ÷ 14 = 1 remainder 5 |
| 5 | 14 ÷ 5 = 2 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 49 and 64 | 3136 |
| 194 and 21 | 4074 |
| 75 and 178 | 13350 |
| 194 and 48 | 4656 |
| 193 and 178 | 34354 |