Least Common Multiple (LCM) of 126 and 97
The least common multiple (LCM) of 126 and 97 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 126 and 97?
First, calculate the GCD of 126 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 97 = 1 remainder 29 |
| 2 | 97 ÷ 29 = 3 remainder 10 |
| 3 | 29 ÷ 10 = 2 remainder 9 |
| 4 | 10 ÷ 9 = 1 remainder 1 |
| 5 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 132 | 8316 |
| 121 and 38 | 4598 |
| 19 and 92 | 1748 |
| 16 and 63 | 1008 |
| 79 and 180 | 14220 |