Least Common Multiple (LCM) of 51 and 93
The least common multiple (LCM) of 51 and 93 is 1581.
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 93?
First, calculate the GCD of 51 and 93 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 51 ÷ 93 = 0 remainder 51 |
| 2 | 93 ÷ 51 = 1 remainder 42 |
| 3 | 51 ÷ 42 = 1 remainder 9 |
| 4 | 42 ÷ 9 = 4 remainder 6 |
| 5 | 9 ÷ 6 = 1 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 21 | 924 |
| 144 and 117 | 1872 |
| 107 and 31 | 3317 |
| 153 and 189 | 3213 |
| 31 and 109 | 3379 |