Least Common Multiple (LCM) of 160 and 113
The least common multiple (LCM) of 160 and 113 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 160 and 113?
First, calculate the GCD of 160 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 160 ÷ 113 = 1 remainder 47 |
| 2 | 113 ÷ 47 = 2 remainder 19 |
| 3 | 47 ÷ 19 = 2 remainder 9 |
| 4 | 19 ÷ 9 = 2 remainder 1 |
| 5 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 49 | 5978 |
| 27 and 44 | 1188 |
| 134 and 60 | 4020 |
| 142 and 170 | 12070 |
| 87 and 161 | 14007 |