Least Common Multiple (LCM) of 97 and 132
The least common multiple (LCM) of 97 and 132 is 12804.
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 132?
First, calculate the GCD of 97 and 132 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 132 = 0 remainder 97 |
| 2 | 132 ÷ 97 = 1 remainder 35 |
| 3 | 97 ÷ 35 = 2 remainder 27 |
| 4 | 35 ÷ 27 = 1 remainder 8 |
| 5 | 27 ÷ 8 = 3 remainder 3 |
| 6 | 8 ÷ 3 = 2 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 40 and 111 | 4440 |
| 91 and 67 | 6097 |
| 135 and 143 | 19305 |
| 75 and 101 | 7575 |
| 196 and 171 | 33516 |