Least Common Multiple (LCM) of 48 and 127
The least common multiple (LCM) of 48 and 127 is 6096.
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 48 and 127?
First, calculate the GCD of 48 and 127 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 48 ÷ 127 = 0 remainder 48 |
| 2 | 127 ÷ 48 = 2 remainder 31 |
| 3 | 48 ÷ 31 = 1 remainder 17 |
| 4 | 31 ÷ 17 = 1 remainder 14 |
| 5 | 17 ÷ 14 = 1 remainder 3 |
| 6 | 14 ÷ 3 = 4 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 147 and 55 | 8085 |
| 196 and 88 | 4312 |
| 54 and 16 | 432 |
| 102 and 139 | 14178 |
| 114 and 115 | 13110 |