Least Common Multiple (LCM) of 12 and 21
The least common multiple (LCM) of 12 and 21 is 84.
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 12 and 21?
First, calculate the GCD of 12 and 21 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 12 ÷ 21 = 0 remainder 12 |
| 2 | 21 ÷ 12 = 1 remainder 9 |
| 3 | 12 ÷ 9 = 1 remainder 3 |
| 4 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 44 and 179 | 7876 |
| 140 and 47 | 6580 |
| 116 and 27 | 3132 |
| 68 and 190 | 6460 |
| 144 and 160 | 1440 |