Least Common Multiple (LCM) of 72 and 159
The least common multiple (LCM) of 72 and 159 is 3816.
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 72 and 159?
First, calculate the GCD of 72 and 159 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 159 = 0 remainder 72 |
| 2 | 159 ÷ 72 = 2 remainder 15 |
| 3 | 72 ÷ 15 = 4 remainder 12 |
| 4 | 15 ÷ 12 = 1 remainder 3 |
| 5 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 199 and 104 | 20696 |
| 42 and 162 | 1134 |
| 117 and 140 | 16380 |
| 47 and 80 | 3760 |
| 122 and 30 | 1830 |