Least Common Multiple (LCM) of 56 and 66
The least common multiple (LCM) of 56 and 66 is 1848.
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 56 and 66?
First, calculate the GCD of 56 and 66 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 56 ÷ 66 = 0 remainder 56 |
| 2 | 66 ÷ 56 = 1 remainder 10 |
| 3 | 56 ÷ 10 = 5 remainder 6 |
| 4 | 10 ÷ 6 = 1 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 39 | 5460 |
| 132 and 117 | 5148 |
| 181 and 177 | 32037 |
| 35 and 111 | 3885 |
| 147 and 95 | 13965 |