Least Common Multiple (LCM) of 27 and 32
The least common multiple (LCM) of 27 and 32 is 864.
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 27 and 32?
First, calculate the GCD of 27 and 32 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 27 ÷ 32 = 0 remainder 27 |
| 2 | 32 ÷ 27 = 1 remainder 5 |
| 3 | 27 ÷ 5 = 5 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 169 and 45 | 7605 |
| 99 and 134 | 13266 |
| 96 and 82 | 3936 |
| 26 and 37 | 962 |
| 168 and 77 | 1848 |