Least Common Multiple (LCM) of 127 and 160
The least common multiple (LCM) of 127 and 160 is 20320.
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 127 and 160?
First, calculate the GCD of 127 and 160 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 127 ÷ 160 = 0 remainder 127 |
| 2 | 160 ÷ 127 = 1 remainder 33 |
| 3 | 127 ÷ 33 = 3 remainder 28 |
| 4 | 33 ÷ 28 = 1 remainder 5 |
| 5 | 28 ÷ 5 = 5 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 163 | 4890 |
| 17 and 24 | 408 |
| 104 and 117 | 936 |
| 31 and 15 | 465 |
| 48 and 122 | 2928 |