Least Common Multiple (LCM) of 32 and 55
The least common multiple (LCM) of 32 and 55 is 1760.
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 32 and 55?
First, calculate the GCD of 32 and 55 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 32 ÷ 55 = 0 remainder 32 |
| 2 | 55 ÷ 32 = 1 remainder 23 |
| 3 | 32 ÷ 23 = 1 remainder 9 |
| 4 | 23 ÷ 9 = 2 remainder 5 |
| 5 | 9 ÷ 5 = 1 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 199 and 56 | 11144 |
| 41 and 170 | 6970 |
| 180 and 84 | 1260 |
| 187 and 94 | 17578 |
| 113 and 85 | 9605 |