Least Common Multiple (LCM) of 101 and 66
The least common multiple (LCM) of 101 and 66 is 6666.
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 101 and 66?
First, calculate the GCD of 101 and 66 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 66 = 1 remainder 35 |
| 2 | 66 ÷ 35 = 1 remainder 31 |
| 3 | 35 ÷ 31 = 1 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 |
|---|---|
| 137 and 114 | 15618 |
| 99 and 199 | 19701 |
| 83 and 24 | 1992 |
| 154 and 125 | 19250 |
| 164 and 53 | 8692 |