Least Common Multiple (LCM) of 49 and 128
The least common multiple (LCM) of 49 and 128 is 6272.
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 49 and 128?
First, calculate the GCD of 49 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 49 ÷ 128 = 0 remainder 49 |
| 2 | 128 ÷ 49 = 2 remainder 30 |
| 3 | 49 ÷ 30 = 1 remainder 19 |
| 4 | 30 ÷ 19 = 1 remainder 11 |
| 5 | 19 ÷ 11 = 1 remainder 8 |
| 6 | 11 ÷ 8 = 1 remainder 3 |
| 7 | 8 ÷ 3 = 2 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 58 | 6322 |
| 190 and 76 | 380 |
| 130 and 126 | 8190 |
| 69 and 108 | 2484 |
| 33 and 114 | 1254 |