Least Common Multiple (LCM) of 51 and 21
The least common multiple (LCM) of 51 and 21 is 357.
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 21?
First, calculate the GCD of 51 and 21 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 51 ÷ 21 = 2 remainder 9 |
| 2 | 21 ÷ 9 = 2 remainder 3 |
| 3 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 128 | 14720 |
| 174 and 59 | 10266 |
| 82 and 103 | 8446 |
| 124 and 28 | 868 |
| 73 and 85 | 6205 |