Least Common Multiple (LCM) of 51 and 66
The least common multiple (LCM) of 51 and 66 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 51 and 66?
First, calculate the GCD of 51 and 66 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 51 ÷ 66 = 0 remainder 51 |
| 2 | 66 ÷ 51 = 1 remainder 15 |
| 3 | 51 ÷ 15 = 3 remainder 6 |
| 4 | 15 ÷ 6 = 2 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 179 and 36 | 6444 |
| 179 and 158 | 28282 |
| 39 and 68 | 2652 |
| 145 and 64 | 9280 |
| 109 and 133 | 14497 |