Least Common Multiple (LCM) of 96 and 159
The least common multiple (LCM) of 96 and 159 is 5088.
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 96 and 159?
First, calculate the GCD of 96 and 159 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 96 ÷ 159 = 0 remainder 96 |
| 2 | 159 ÷ 96 = 1 remainder 63 |
| 3 | 96 ÷ 63 = 1 remainder 33 |
| 4 | 63 ÷ 33 = 1 remainder 30 |
| 5 | 33 ÷ 30 = 1 remainder 3 |
| 6 | 30 ÷ 3 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 89 | 10947 |
| 74 and 175 | 12950 |
| 13 and 136 | 1768 |
| 59 and 48 | 2832 |
| 150 and 192 | 4800 |