Least Common Multiple (LCM) of 27 and 45
The least common multiple (LCM) of 27 and 45 is 135.
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 45?
First, calculate the GCD of 27 and 45 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 27 ÷ 45 = 0 remainder 27 |
| 2 | 45 ÷ 27 = 1 remainder 18 |
| 3 | 27 ÷ 18 = 1 remainder 9 |
| 4 | 18 ÷ 9 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 83 and 20 | 1660 |
| 191 and 120 | 22920 |
| 30 and 53 | 1590 |
| 169 and 81 | 13689 |
| 115 and 16 | 1840 |