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 |
|---|---|
| 186 and 50 | 4650 |
| 123 and 87 | 3567 |
| 114 and 133 | 798 |
| 133 and 150 | 19950 |
| 188 and 133 | 25004 |