Least Common Multiple (LCM) of 105 and 27
The least common multiple (LCM) of 105 and 27 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 105 and 27?
First, calculate the GCD of 105 and 27 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 27 = 3 remainder 24 |
| 2 | 27 ÷ 24 = 1 remainder 3 |
| 3 | 24 ÷ 3 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 163 and 21 | 3423 |
| 119 and 72 | 8568 |
| 170 and 12 | 1020 |
| 55 and 147 | 8085 |
| 85 and 114 | 9690 |