Least Common Multiple (LCM) of 66 and 52
The least common multiple (LCM) of 66 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 66 and 52?
First, calculate the GCD of 66 and 52 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 66 ÷ 52 = 1 remainder 14 |
| 2 | 52 ÷ 14 = 3 remainder 10 |
| 3 | 14 ÷ 10 = 1 remainder 4 |
| 4 | 10 ÷ 4 = 2 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 81 and 63 | 567 |
| 142 and 147 | 20874 |
| 13 and 65 | 65 |
| 103 and 64 | 6592 |
| 15 and 136 | 2040 |