Least Common Multiple (LCM) of 56 and 132
The least common multiple (LCM) of 56 and 132 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 132?
First, calculate the GCD of 56 and 132 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 56 ÷ 132 = 0 remainder 56 |
| 2 | 132 ÷ 56 = 2 remainder 20 |
| 3 | 56 ÷ 20 = 2 remainder 16 |
| 4 | 20 ÷ 16 = 1 remainder 4 |
| 5 | 16 ÷ 4 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 177 and 59 | 177 |
| 110 and 46 | 2530 |
| 129 and 129 | 129 |
| 102 and 89 | 9078 |
| 150 and 165 | 1650 |