Least Common Multiple (LCM) of 127 and 27
The least common multiple (LCM) of 127 and 27 is 3429.
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 127 and 27?
First, calculate the GCD of 127 and 27 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 127 ÷ 27 = 4 remainder 19 |
| 2 | 27 ÷ 19 = 1 remainder 8 |
| 3 | 19 ÷ 8 = 2 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 |
|---|---|
| 115 and 47 | 5405 |
| 13 and 67 | 871 |
| 129 and 23 | 2967 |
| 146 and 92 | 6716 |
| 157 and 68 | 10676 |