Least Common Multiple (LCM) of 97 and 144
The least common multiple (LCM) of 97 and 144 is 13968.
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 144?
First, calculate the GCD of 97 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 144 = 0 remainder 97 |
| 2 | 144 ÷ 97 = 1 remainder 47 |
| 3 | 97 ÷ 47 = 2 remainder 3 |
| 4 | 47 ÷ 3 = 15 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 42 | 2814 |
| 78 and 55 | 4290 |
| 170 and 140 | 2380 |
| 111 and 59 | 6549 |
| 140 and 184 | 6440 |