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 |
|---|---|
| 56 and 160 | 1120 |
| 76 and 153 | 11628 |
| 178 and 91 | 16198 |
| 76 and 144 | 2736 |
| 122 and 96 | 5856 |