Least Common Multiple (LCM) of 23 and 51
The least common multiple (LCM) of 23 and 51 is 1173.
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 23 and 51?
First, calculate the GCD of 23 and 51 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 23 ÷ 51 = 0 remainder 23 |
| 2 | 51 ÷ 23 = 2 remainder 5 |
| 3 | 23 ÷ 5 = 4 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 168 and 67 | 11256 |
| 100 and 128 | 3200 |
| 21 and 126 | 126 |
| 104 and 192 | 2496 |
| 59 and 48 | 2832 |