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 |
|---|---|
| 146 and 178 | 12994 |
| 22 and 18 | 198 |
| 114 and 42 | 798 |
| 193 and 147 | 28371 |
| 41 and 48 | 1968 |