Least Common Multiple (LCM) of 45 and 159
The least common multiple (LCM) of 45 and 159 is 2385.
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 45 and 159?
First, calculate the GCD of 45 and 159 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 159 = 0 remainder 45 |
| 2 | 159 ÷ 45 = 3 remainder 24 |
| 3 | 45 ÷ 24 = 1 remainder 21 |
| 4 | 24 ÷ 21 = 1 remainder 3 |
| 5 | 21 ÷ 3 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 111 | 4773 |
| 190 and 162 | 15390 |
| 196 and 103 | 20188 |
| 96 and 113 | 10848 |
| 80 and 68 | 1360 |