Least Common Multiple (LCM) of 27 and 49
The least common multiple (LCM) of 27 and 49 is 1323.
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 49?
First, calculate the GCD of 27 and 49 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 27 ÷ 49 = 0 remainder 27 |
| 2 | 49 ÷ 27 = 1 remainder 22 |
| 3 | 27 ÷ 22 = 1 remainder 5 |
| 4 | 22 ÷ 5 = 4 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 178 and 153 | 27234 |
| 50 and 92 | 2300 |
| 62 and 65 | 4030 |
| 105 and 169 | 17745 |
| 131 and 47 | 6157 |