Least Common Multiple (LCM) of 97 and 126
The least common multiple (LCM) of 97 and 126 is 12222.
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 126?
First, calculate the GCD of 97 and 126 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 126 = 0 remainder 97 |
| 2 | 126 ÷ 97 = 1 remainder 29 |
| 3 | 97 ÷ 29 = 3 remainder 10 |
| 4 | 29 ÷ 10 = 2 remainder 9 |
| 5 | 10 ÷ 9 = 1 remainder 1 |
| 6 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 187 and 27 | 5049 |
| 197 and 162 | 31914 |
| 113 and 72 | 8136 |
| 106 and 38 | 2014 |
| 115 and 135 | 3105 |