Least Common Multiple (LCM) of 49 and 160
The least common multiple (LCM) of 49 and 160 is 7840.
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 160?
First, calculate the GCD of 49 and 160 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 49 ÷ 160 = 0 remainder 49 |
| 2 | 160 ÷ 49 = 3 remainder 13 |
| 3 | 49 ÷ 13 = 3 remainder 10 |
| 4 | 13 ÷ 10 = 1 remainder 3 |
| 5 | 10 ÷ 3 = 3 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 192 | 192 |
| 142 and 53 | 7526 |
| 80 and 30 | 240 |
| 146 and 78 | 5694 |
| 70 and 13 | 910 |