Least Common Multiple (LCM) of 51 and 23
The least common multiple (LCM) of 51 and 23 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 51 and 23?
First, calculate the GCD of 51 and 23 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 51 ÷ 23 = 2 remainder 5 |
| 2 | 23 ÷ 5 = 4 remainder 3 |
| 3 | 5 ÷ 3 = 1 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 55 | 6435 |
| 198 and 119 | 23562 |
| 132 and 44 | 132 |
| 176 and 92 | 4048 |
| 163 and 51 | 8313 |