Least Common Multiple (LCM) of 97 and 159
The least common multiple (LCM) of 97 and 159 is 15423.
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 97 and 159?
First, calculate the GCD of 97 and 159 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 159 = 0 remainder 97 |
| 2 | 159 ÷ 97 = 1 remainder 62 |
| 3 | 97 ÷ 62 = 1 remainder 35 |
| 4 | 62 ÷ 35 = 1 remainder 27 |
| 5 | 35 ÷ 27 = 1 remainder 8 |
| 6 | 27 ÷ 8 = 3 remainder 3 |
| 7 | 8 ÷ 3 = 2 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 77 | 1155 |
| 116 and 67 | 7772 |
| 11 and 33 | 33 |
| 25 and 128 | 3200 |
| 59 and 108 | 6372 |