Least Common Multiple (LCM) of 160 and 103
The least common multiple (LCM) of 160 and 103 is 16480.
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 160 and 103?
First, calculate the GCD of 160 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 160 ÷ 103 = 1 remainder 57 |
| 2 | 103 ÷ 57 = 1 remainder 46 |
| 3 | 57 ÷ 46 = 1 remainder 11 |
| 4 | 46 ÷ 11 = 4 remainder 2 |
| 5 | 11 ÷ 2 = 5 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 63 and 53 | 3339 |
| 21 and 112 | 336 |
| 82 and 128 | 5248 |
| 180 and 183 | 10980 |
| 107 and 25 | 2675 |