Least Common Multiple (LCM) of 163 and 72
The least common multiple (LCM) of 163 and 72 is 11736.
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 72?
First, calculate the GCD of 163 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 163 ÷ 72 = 2 remainder 19 |
| 2 | 72 ÷ 19 = 3 remainder 15 |
| 3 | 19 ÷ 15 = 1 remainder 4 |
| 4 | 15 ÷ 4 = 3 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 130 | 13910 |
| 76 and 88 | 1672 |
| 113 and 179 | 20227 |
| 132 and 149 | 19668 |
| 172 and 164 | 7052 |