Least Common Multiple (LCM) of 27 and 35
The least common multiple (LCM) of 27 and 35 is 945.
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 35?
First, calculate the GCD of 27 and 35 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 27 ÷ 35 = 0 remainder 27 |
| 2 | 35 ÷ 27 = 1 remainder 8 |
| 3 | 27 ÷ 8 = 3 remainder 3 |
| 4 | 8 ÷ 3 = 2 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 154 and 30 | 2310 |
| 188 and 47 | 188 |
| 194 and 188 | 18236 |
| 39 and 58 | 2262 |
| 123 and 153 | 6273 |