Least Common Multiple (LCM) of 97 and 180
The least common multiple (LCM) of 97 and 180 is 17460.
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 180?
First, calculate the GCD of 97 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 180 = 0 remainder 97 |
| 2 | 180 ÷ 97 = 1 remainder 83 |
| 3 | 97 ÷ 83 = 1 remainder 14 |
| 4 | 83 ÷ 14 = 5 remainder 13 |
| 5 | 14 ÷ 13 = 1 remainder 1 |
| 6 | 13 ÷ 1 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 76 and 15 | 1140 |
| 99 and 39 | 1287 |
| 69 and 126 | 2898 |
| 118 and 157 | 18526 |
| 61 and 109 | 6649 |