Least Common Multiple (LCM) of 52 and 66
The least common multiple (LCM) of 52 and 66 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 52 and 66?
First, calculate the GCD of 52 and 66 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 52 ÷ 66 = 0 remainder 52 |
| 2 | 66 ÷ 52 = 1 remainder 14 |
| 3 | 52 ÷ 14 = 3 remainder 10 |
| 4 | 14 ÷ 10 = 1 remainder 4 |
| 5 | 10 ÷ 4 = 2 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 32 | 800 |
| 43 and 54 | 2322 |
| 109 and 151 | 16459 |
| 173 and 104 | 17992 |
| 121 and 71 | 8591 |