Least Common Multiple (LCM) of 66 and 102
The least common multiple (LCM) of 66 and 102 is 1122.
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 102?
First, calculate the GCD of 66 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 66 ÷ 102 = 0 remainder 66 |
| 2 | 102 ÷ 66 = 1 remainder 36 |
| 3 | 66 ÷ 36 = 1 remainder 30 |
| 4 | 36 ÷ 30 = 1 remainder 6 |
| 5 | 30 ÷ 6 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 65 | 12480 |
| 144 and 72 | 144 |
| 183 and 48 | 2928 |
| 114 and 23 | 2622 |
| 142 and 117 | 16614 |