Least Common Multiple (LCM) of 66 and 49
The least common multiple (LCM) of 66 and 49 is 3234.
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 49?
First, calculate the GCD of 66 and 49 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 66 ÷ 49 = 1 remainder 17 |
| 2 | 49 ÷ 17 = 2 remainder 15 |
| 3 | 17 ÷ 15 = 1 remainder 2 |
| 4 | 15 ÷ 2 = 7 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 136 and 17 | 136 |
| 127 and 122 | 15494 |
| 139 and 21 | 2919 |
| 78 and 11 | 858 |
| 133 and 117 | 15561 |