Least Common Multiple (LCM) of 163 and 180
The least common multiple (LCM) of 163 and 180 is 29340.
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 163 and 180?
First, calculate the GCD of 163 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 163 ÷ 180 = 0 remainder 163 |
| 2 | 180 ÷ 163 = 1 remainder 17 |
| 3 | 163 ÷ 17 = 9 remainder 10 |
| 4 | 17 ÷ 10 = 1 remainder 7 |
| 5 | 10 ÷ 7 = 1 remainder 3 |
| 6 | 7 ÷ 3 = 2 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 10 and 106 | 530 |
| 164 and 186 | 15252 |
| 143 and 154 | 2002 |
| 117 and 137 | 16029 |
| 64 and 113 | 7232 |