Least Common Multiple (LCM) of 160 and 109
The least common multiple (LCM) of 160 and 109 is 17440.
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 109?
First, calculate the GCD of 160 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 160 ÷ 109 = 1 remainder 51 |
| 2 | 109 ÷ 51 = 2 remainder 7 |
| 3 | 51 ÷ 7 = 7 remainder 2 |
| 4 | 7 ÷ 2 = 3 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 70 and 97 | 6790 |
| 63 and 129 | 2709 |
| 33 and 110 | 330 |
| 24 and 117 | 936 |
| 52 and 30 | 780 |