Least Common Multiple (LCM) of 21 and 54
The least common multiple (LCM) of 21 and 54 is 378.
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 21 and 54?
First, calculate the GCD of 21 and 54 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 54 = 0 remainder 21 |
| 2 | 54 ÷ 21 = 2 remainder 12 |
| 3 | 21 ÷ 12 = 1 remainder 9 |
| 4 | 12 ÷ 9 = 1 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 156 and 172 | 6708 |
| 199 and 185 | 36815 |
| 187 and 111 | 20757 |
| 196 and 192 | 9408 |
| 67 and 130 | 8710 |