Least Common Multiple (LCM) of 12 and 97
The least common multiple (LCM) of 12 and 97 is 1164.
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 12 and 97?
First, calculate the GCD of 12 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 12 ÷ 97 = 0 remainder 12 |
| 2 | 97 ÷ 12 = 8 remainder 1 |
| 3 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 194 and 131 | 25414 |
| 105 and 49 | 735 |
| 162 and 125 | 20250 |
| 150 and 36 | 900 |
| 125 and 85 | 2125 |