Least Common Multiple (LCM) of 51 and 132
The least common multiple (LCM) of 51 and 132 is 2244.
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 132?
First, calculate the GCD of 51 and 132 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 51 ÷ 132 = 0 remainder 51 |
| 2 | 132 ÷ 51 = 2 remainder 30 |
| 3 | 51 ÷ 30 = 1 remainder 21 |
| 4 | 30 ÷ 21 = 1 remainder 9 |
| 5 | 21 ÷ 9 = 2 remainder 3 |
| 6 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 23 and 138 | 138 |
| 196 and 179 | 35084 |
| 66 and 151 | 9966 |
| 69 and 106 | 7314 |
| 175 and 195 | 6825 |