Least Common Multiple (LCM) of 126 and 160
The least common multiple (LCM) of 126 and 160 is 10080.
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 126 and 160?
First, calculate the GCD of 126 and 160 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 160 = 0 remainder 126 |
| 2 | 160 ÷ 126 = 1 remainder 34 |
| 3 | 126 ÷ 34 = 3 remainder 24 |
| 4 | 34 ÷ 24 = 1 remainder 10 |
| 5 | 24 ÷ 10 = 2 remainder 4 |
| 6 | 10 ÷ 4 = 2 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 179 and 175 | 31325 |
| 54 and 182 | 4914 |
| 102 and 36 | 612 |
| 47 and 177 | 8319 |
| 25 and 112 | 2800 |