Least Common Multiple (LCM) of 66 and 97
The least common multiple (LCM) of 66 and 97 is 6402.
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 66 and 97?
First, calculate the GCD of 66 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 66 ÷ 97 = 0 remainder 66 |
| 2 | 97 ÷ 66 = 1 remainder 31 |
| 3 | 66 ÷ 31 = 2 remainder 4 |
| 4 | 31 ÷ 4 = 7 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 43 and 96 | 4128 |
| 179 and 88 | 15752 |
| 87 and 127 | 11049 |
| 38 and 39 | 1482 |
| 192 and 175 | 33600 |