Least Common Multiple (LCM) of 27 and 77
The least common multiple (LCM) of 27 and 77 is 2079.
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 77?
First, calculate the GCD of 27 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 27 ÷ 77 = 0 remainder 27 |
| 2 | 77 ÷ 27 = 2 remainder 23 |
| 3 | 27 ÷ 23 = 1 remainder 4 |
| 4 | 23 ÷ 4 = 5 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 24 | 4200 |
| 86 and 74 | 3182 |
| 30 and 40 | 120 |
| 172 and 56 | 2408 |
| 67 and 68 | 4556 |