Least Common Multiple (LCM) of 113 and 160
The least common multiple (LCM) of 113 and 160 is 18080.
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 113 and 160?
First, calculate the GCD of 113 and 160 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 160 = 0 remainder 113 |
| 2 | 160 ÷ 113 = 1 remainder 47 |
| 3 | 113 ÷ 47 = 2 remainder 19 |
| 4 | 47 ÷ 19 = 2 remainder 9 |
| 5 | 19 ÷ 9 = 2 remainder 1 |
| 6 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 120 | 960 |
| 87 and 12 | 348 |
| 67 and 98 | 6566 |
| 24 and 60 | 120 |
| 127 and 68 | 8636 |